Here is how the three gospel accounts put it (Jesus' wilderness temptation that is):
Mt 4:1 - 3: "Then Jesus was led by the spirit up into the wilderness to be tempted by the Devil. 2 After he had fasted forty days and forty nights, then he felt hungry. 3 Also, the Tempter came and said to him: ..."
Mk 1:12, 13: "And immediately the spirit impelled him to go into the wilderness. 13 So he continued in the wilderness forty days, being tempted by Satan, and he was with the wild beasts, but the angels were ministering to him."
Lk 4:1 - 3: "Now Jesus, full of holy spirit, turned away from the Jordan, and he was led about by the spirit in the wilderness 2 for forty days, while being tempted by the Devil. Furthermore, he ate nothing in those days, and so, when they were concluded, he felt hungry. 3 At this the Devil said to him:..."
Together they allow for the idea that Jesus was tempted all (or part of) 40 days. And in fact, they state that was the purpose of his being sent into the wilderness. Luke's account ends with this statement: "So the Devil, having concluded all the temptation, retired from him until another convenient time." (4:13) So this was not the end of Jesus being tempted by Satan. In fact, he (Jesus) saw Peter's words as a form of Satan's temptation in Mt chapter 16:21-23. Not that Satan had necessarily 'entered' Peter like is later said of Judas, but the context says that Peter was influenced by 'the thoughts of men,' who had themselves been influenced by Satan.
I thought Tec (Tammy) made some good comments about Satan's tempting of Jesus and about whether he wanted him dead or not. I had some thoughts on this as well but unfortunately I have to go (not to the bathroom) at the moment.