ThiChi....I hedge my posts a lot, just to make sure I'm not stating things as facts, though I probably don't need to, since literary dependence in this case is clear. How do we know this is a case of literary dependence? Because the allusions in the Temptation narrative are all to just one book of the Torah (Deuteronomy), and aside from the vision on the mountain are all clustered to one small section of the book and are even told mostly in the same order. There are verbal parallels, where again the wording has been influenced by the Deuteronomy text (and not the original Hebrew, but a Greek translation), and even a few formal quotations which should remove all doubt on the dependence. According to the rules of literary analysis, the text fully qualifies as an instance of literary borrowing. So whether you believe the story in Q really happened, it is still clear the author of Q used Deuteronomy to tell and phrase the story. And it isn't the original Hebrew texts that is used to inspire the wording of the story, but the Greek translation which worded things a particular way. So in one sense, we can readily see that it isn't simply "OT events" in the Hebrew Bible that foretold the story that then Q relates, but rather a specific Greek translation written hundreds of years later that was an immediate source of such allusions as Jesus seeing the kingdoms of the world from a mountain, which follows directly the wording in the Greek. And it isn't just the use of a much later Greek translation, but also extrabiblical Jewish tradition that is used in Q, such as Satan being present with the Israelites in the wilderness which is nowhere stated as such in Deuteronomy or the OT. This is readily explained, most simply, by saying that the author of Q is simply constructing his narrative by borrowing from Deuteronomy (mostly one specific section of the book) and extrabiblical tradition.
Now if you know a little bit about haggadah, midrash, apocalyptic literature, and so forth, you can see that this is far from unusual in Jewish writing. We find it time and time again, in both extrabiblical texts and biblical ones as well. To use an example from the OT, the fleeing Jonah lies down and falls fast asleep (wyskb wyrdm) in Jonah 1:5. In 1 Kings 19:5, another prophet, Elijah, who is also fleeing, lies down and falls asleep (wyskb wyysd). This by itself would not be sufficient proof that Jonah is recalling the story of Elijah, except that three chapters later, Jonah contains lines that strongly recall 1 Kings 19:4:
1 Kings 19:4: Elijah "went a day's journey into the wilderness, and came and sat down under a solitary broom tree. He asked that he might die saying (wys'l 't-npsw lmwt wy'mr), 'It is enough; now, O Yahweh, take away my life for ('th yhwh qch npsy ky) I am no better than my ancestors".
Jonah 4:3: "And now, O Yahweh, please take my life from me, for ('t-npsy mmny ky w'th yhwh qch-n') it is better for me to die than to live".
Jonah 4:8: Jonah "asked that he die, saying (wys'l 't-npsw lmwt wy'mr), 'It is better for me to die than to live".
There is also a broader thematic correspondence between Jonah and Elijah: both are dejected, disillusioned prophets who, while sitting beneath a plant, ask to die and have a dialogue with God. There is even a coincidence of numbers. Elijah first takes a day's journey into the wilderness (1 Kings 19:4), and then a 40-day journey (1 Kings 19:8), whereas Jonah fortells Ninevah's destruction 40 days after his day's journey into the city (Jonah 3:4). There are other correspondences that I won't get into, but all this is sufficient to show that the Jonah story is literarily dependent on the Elijah story in 1 Kings. The Elijah story was certainly not a prophecy of Jonah that was fulfilled in Jonah; it is simply a case of motifs and even dialogue from one story being copied and used to construct a different story about someone else. The story of Jesus and the fig tree in Mark 11:12-22, on the other hand, appears to be influenced by the story in Jonah of the curse declared on Jonah's castor-oil plant (Jonah 4:5-10 ). Jonah was in ill spirits because God did not attack Ninevah as he had warned and God made a castor-oil plant to grow over his head to give him shade and soothe his temper. The story continues: "But at dawn the next day, God arranged that a worm would attack the castor-oil plant -- and it withered (apexeranthe)" (Jonah 4:6; LXX). The story in Mark relates how Jesus cursed a fig tree and then, "as they passed by in the morning, they saw the fig tree withered away (exerantai, the same root as apexeranthe in Jonah) to its roots" (Mark 11:21).
And neither are these isolated incidents. Dale Allison has a whole book on the intertextuality between the OT and Q, JD Crossan has written extensively on the intertextuality in the Passion narrative, and so forth. I have previously written on the whole story of Judas Iscariot and the arrest of Jesus draws on OT passages [1], how the hand-washing scene with Pilate draws on Deuteronomy and Psalm 26 [2], how the story of Jesus as an exorcist draws on language about Moses from Exodus and extrabiblical tradition [3], how the story of the Faithful and Wise Servant draws directly on the story of Joseph from Genesis [4], and how the stories of the Miracle at Cana and the Woman at the Well in John 2, 4 draw on OT motifs surrounding Isaac, Jacob, and Moses [5]. Some interesting parallels in the latter example:
"When all Egypt began to feel the famine, the people cried to Pharaoh for food. Then Pharaoh told all the Egyptians: 'Go to Joseph and do what he tells you (ho ean eipe humin poiesate).' " (Genesis 41:55; LXX)
"When the wine gave out, the mother of Jesus said to him, 'They have no wine'... His mother said to the servants, 'Do whatever he tell you (ho ti an lego humin poiesate).' " (John 2:3, 5)
"He also performed (epoiese) the signs (ta semeia) before the people, and they believed (episteusen ). And when they heard that the Lord was concerned about them and had seen their misery, they bowed down and worshipped.... And when the Israelites saw the great power of the Lord displayed (epoiese) against the Egyptians, the people feared the Lord and believed in him (episteusan eis auton) and in Moses his servant." (Exodus 4:30-31; 14:31)
"This was the first of the signs (ton semeion) Jesus performed (epoiesen) in Cana of Galilee, and manifested his glory, and his disciples believed in him (episteusan eis auton).... Many other signs (semeia) Jesus also performed (epoiesen) in the presence of his disciples, which are not written in this book; but these have been written that you may believe (pisteuete) that Jesus is the Christ, the Son of God." (John 2:11; 20:30-31)
"I will strike the water (to hudor) of the river and it shall be changed (metabalei) to blood.... Take your staff and stretch out your hand over the waters (ta hudata) of Egypt, over their rivers and their canals, their reedy places (ta hele auton), and all their reservoirs, and let them become (egeneto) blood throughout the land of Egypt, even down to the contents of every tub and jar (lithois).... [Moses] struck the waters (to hudor) of the river, and all the water (to hudor) in the river changed (metebalen) to blood. The fish in the river died, and the river smelt so foul that the Egyptians found it impossible to drink its water (piein hudor)." (Exodus 7:17, 19-21)
"Now there were six stone water jars (lithinai hudrai) set there.... Jesus said to them, 'Fill the water jars (hudrias) with water (hudatos ).' And they filled them to the brim. And he said to them, 'Draw some out now, and take it to the head waiter.' And they took it to him. And when the head waiter tasted the water (egeusato to hudor) which had become (gegenemenon) wine, and did not know where it came from, but the servants who had drawn the water knew, the headwaiter called the bridegroom." (John 2:7-9)
"In the evening, at the time when the water bearers go down for water (tou hudatos), he made the camels kneel outside the town (tes poleos) near the well (phrear)...[Rebekah] had a water jar (hudrian) on her shoulder. The girl (gunaikos) was very beautiful, and a virgin; no man had touched her. She went down to the well (pegen), filled her water jar (hudrian) and came up again. Running to meet her, the servant said, 'Please give me (potisan me) a little water (hudor) from your water jar (hudrias sou).' She said, 'Drink, my lord (pie kurie),' and she quickly lowered her water jar (hudrian) on her arm and gave him a drink (epotisan)....She quickly emptied her jar into the trough, and ran to the well again to draw (antlesai).... 'I said to her, "Please give me a drink (de potisan me)". Quickly she lowered her water jar (hudrian autes) saying, "Drink (pie su), and I will water your camels too." '.... Isaac, who lived in the Negeb, had meanwhile come into the wilderness of the well (phrear) of Lahai Roi. Now Isaac went walking in the fields as evening fell, and lifting up his eyes (anablepsasa tois ophthalmois) saw camels coming (erkhomenas). And Rebekah lifted up her eyes (anablepsasa tois ophthalmois) and saw Isaac. She jumped down from her camel, and asked the servant, 'Who is that man walking into the fields (eis to pedion ) to meet us?' The servant replied, 'That is my master'; then she took her veil and hid her face. The servant told Isaac the whole story, and Isaac led Rebekah into his tent and he married Rebekah." (Genesis 24:11, 15-19, 45-46, 62-67)
"He left Judea and departed again into Galilee. And he had to pass through Samaria. So he came to a city (eis polin) of Samaria called Sychar, near the parcel of ground that Jacob gave to his son Joseph; and Jacob's well (pege) was there. Jesus, being weary from his journey, was sitting thus by the well (pege). It was about the sixth hour [i.e. 6 pm]. There came (erkhetai) a woman (gune) of Samaria to draw water (antlesai hudor). Jesus said to her, 'Give me a drink (dos moi pein).' For his disciples had gone away to the city to buy food.... She said to him, 'Lord (kurie), you have no bucket (antlema) and the well (phrear) is deep; where then do you get that living water? You are not greater than our father Jacob who gave us the well (phrear), and drank (epien) of it himself, and his sons, and this cattle?' ... So the woman left her water jar (hudrian autes), and went into the city....'Behold, I say to you, open up your eyes (eparate tous ophthalmous humon), and look into the fields (theasasthe tas khoras).' " (John 4:3-8, 11-12, 28, 35)
"When Pharaoh (Pharao) heard (ekouse) of this, he tried to kill (ezetei anelein) Moses, but Moses fled from Pharaoh and went (elthon) to live in Midian, where he sat down (ekathisen) by a well (epi tou phreatos). Now the priest of Midian had seven daughters. They came to draw water (entloun ) and fill the troughs to water their father's sheep. Shepherds came and drove them away, but Moses came to their defense and watered their sheep for them.... So Moses settled with this man, who gave him his daughter Zipporah in marriage ." (Exodus 2:15-17, 21).
"The Pharisees (Pharisaio) heard (ekousan ) that Jesus was gaining and baptizing more disciples than John, although in fact it was not Jesus who baptized, but his disciples. When the Lord learned of this, he left Judea and went back (apelthen ) once more to Galilee. Now he had to go through Samaria. So he came to a town in Samaria called Sychar, near the parcel of ground Jacob gave to his son Joseph, and Jacob's well was there. Jesus, being weary from his journey, sat down (ekathezeto) by the well (epi te pege). It was about the sixth hour. There came a woman of Samaria to draw water (antlesai hudor)." "For this reason the Jews tried harder to kill (mallon ezetoun apokteinai) him." (John 4:1-7; 5:18)
In many of these examples, the allusion is not simply to the events of OT passages but to specific wordings, and it isn't the original Hebrew text that anticipates the gospel wordings but the much later Greek translation. Some of the above examples also draw on extrabiblical tradition, again showing that it isn't the OT events per se that directly influenced the NT text but the literary tradition, both canonical and extracanonical.
And whether you believe that the Temptation in the Wilderness story is historical, you can believe that as a matter of faith, but the historian has certain rules of evidence in determining historicity. And borrowing narrative, dialogue, and specific motifs and details from OT sources and folklore is usually regarded as evidence against historicity, not just in the case of the Jesus but in any study of separating history from legend. Thus, in a separate thread, I showed how the earliest poem on the King Arthur legend incorporated folkloric material from Celtic legend, suggesting that they do not represent events from the life of the historical Arthur (if one existed). Just going by Occam's Razor, we can account for the entirety of the Q Temptation story through allusions and quotations to Deuteronomy and extrabiblical tradition. It is simpler to just regard it as a story that was constructed through OT intertextuality rather say that it was written through OT allusion as well as (1) faithfully representing a historical event wherein all the described events happened, and (2) these events just happened to correspond to both OT events and the way they are described in later translation and characterized in extrabiblical tradition. It's the kind of story that, if it were a case of an ancient Greek romance extensively alluding and quoting the Iliad, a historian would regard as historically doubtful.