Did they have some faith of going to heaven? I don't remember reading about this in the OT.
Yes, many Jews had this hope -- either a more Hellenistic view of a person's soul going to heaven at death (either as final destiny or as an intermediate state prior to resurrection), or a view that the righteous in the resurrection would be raised in a glorious, incorruptible, angelic existence and/or live in God's presence in heaven. And other Jews had other ideas. There was no "one" thing that the "Jews" believed. And most of this eschatology developed in the period between the OT and the NT, although it is found in the latest parts of the OT (such as Daniel).
Here are some statements in early Judaism on this subject:
"Many of those who sleep in the dusty earth will awake, some to everlasting life and some to reproach and everlasting disgrace. The wise will shine like the splendor of the firmament, and those who lead the common people to righteousness like the stars forever and ever" (Daniel 12:2-3; written in the early second century BC).
"To those whom God has selected he has given them as everlasting possession; and he has given them an inheritance in the lot of the holy ones [i.e. the angels]. He unites their assembly to the sons of the heavens in order to form the council of the community and a foundation of the building of holiness to be an everlasting planting throughout all future ages" (1QS 11:7-8; written in the late second century BC).
"I give thanks to you, O Lord, for you have redeemed me from the pit and from Sheol Abaddon you have lifted me to an eternal height ... to be stationed with the host of the holy ones and to enter into fellowship with the congregation of the children of heaven" (1QH 3:19-23; written in the late second century BC).
"You will shine like the lights of heaven and you will be seen, and the gate of heaven will be opened to you...You are about to make a great rejoicing like the angels of heaven. You shall not have to hide on the day of the great judgment, and you shall not be found as the sinners; but the eternal judgment will be far away from you for all the generations of the world. Now, fear not, righteous ones, when you see the sinners waxing strong and flourishing ... for you will be associates with the host of heaven" (1 Enoch 104:2-6; written in the early first century BC).
"But the souls of the just are in the hand of God, and no torment shall touch them. They seemed, in the view of the foolish, to be dead; and their passing away was thought an affliction and their going forth from us, utter destruction. But they are in peace. For if before men, indeed, they be punished, yet is their hope full of immortality, chastised a little, they shall be greatly blessed, because God tried them and found them worthy of himself. As gold in the furnace, he proved them, and as sacrificial offerings he took them to himself. In the time of their visitation they shall shine, and shall dart about as sparks through stubble. They shall judge nations and rule over peoples, and the Lord shall be their King forever" (Wisdom 3:1-8, cf. 5:5; written in the first century BC).
"Those who fear the Lord shall rise up to eternal life, and their life shall be in the Lord's light and it shall never end....To those who live in the righteousness of his commandments, in the Law, which he has commanded for our life, the Lord's devout shall live by it forever, in the Lord's paradise, the trees of life are his devout ones. Their planting is firmly rooted forever, they shall not be uprooted as long as the heavens shall last, for Israel is the portion and inheritance of God" (Psalms of Solomon 14:1-4; written in the first century BC)
"The heavens will be opened and from the temple of glory sanctification will come upon him with a fatherly voice, as from Abraham to Isaac...And he shall open the gates of paradise, he shall remove the sword that that has threatened since Adam, and he will grant the saints to eat of the tree of life. The spirit of holiness shall be upon them and Beliar shall be bound by him... Then Abraham, Isaac, and Jacob will rejoice, and I shall be glad, and all the saints will be clothed in righteousness" (Testament of Levi 18:7, 10-14; written in first century BC)
"He will make war against Beliar, he will grant the vengeance of victory as our goal. And he shall take from Beliar the captives, the souls of the saints, and he shall turn the hearts of the disobedient ones to the Lord and grant eternal peace to those who call upon him. And the saints shall refresh themselves in Eden, and the righteous shall rejoice in the New Jerusalem which shall be eternally for the glorification of God" (Testament of Dan 5:10-12; written in the first century BC).
"And there I saw another vision, the dwellings of the holy ones, and the resting places of the righteous. There my eyes saw their dwellings with the holy angels and their resting places with the holy ones, and they interceded and petitioned on behalf of the children of the people, and righteousness flowed before them like water, and mercy like dew on the earth, and thus it is in their midst forever and ever. And in those days my eyes saw the chosen one with righteousness and faith, and righteousness shall prevail in his days, and the righteous and chosen ones shall be without number before him forever and ever, and I saw a dwelling place underneath the wings of the Lord of Spirits, and all the righteous and the elect before him shall be as intense as the light of fire....There I wanted to dwell and my soul desired that dwelling place. Already my portion is there, for thus it has been reserved for me before the Lord of Spirits" (1 Enoch 39:4-8; written in the early first century AD).
"Then his kingdom will appear throughout his creation. Then the devil will have an end...The sun will not give light and in darkness the horns of the moon will flee, broken into pieces and turned wholly to blood. Even the circle of the stars will be thrown into disarray...For God Most High will surge forth, the Eternal One alone. In full view will he come to work vengeance on the nations and all their idols will be destroy. Then you will be happy, O Israel! And you will mount above the necks and the wings of an eagle. And all things will be fulfilled. And God will raise you to the heights, and he will fix you firmly in the heaven of the stars, in the place of his habitations. And you will behold from on high and see your enemies on the earth and you will rejoice in recognizing them" (Assumption of Moses 10:1-10; written in the early first century AD).
"Let us arm ourselves with the control over the passions which comes from divine reason. After our death in this fashion Abraham and Isaac and Jacob will receive us, and all our forefathers will prase us....With these words the mother of the seven exhorted each one and persuaded them to die rather than transgress the commandment of God, and they knew full well themselves that those who die for the sake of God live unto God, as do Abraham and Isaac and Jacob and all the patriarchs. Some of the guards declared that when she, too, was about to be seized and put to death, she threw herself into the fire so that no one would touch her body. O mother with the seven sons, who broke down the violance of the tyrant and thwarted his wicked devices....Be of good cheer, therefore, mother of holy soul, whose hope of endurance is secure with God. Not so majestic stands the moon in heaven as you stand, lighting the way to piety for your seven starlike sons, honored by God and firmly set with them in heaven....The sons of Abraham, together with their mother, who won the victor's prize, are gathered together in the choir of their fathers, having received pure and deathless souls from God, to whom be glory frever and ever" (4 Maccabees 13:16-17, 16:24-25, 17:1-5, 18:23; written in the middle of the first century AD).
"The Lord of all, sitting on his holy throne, stretched out of hands and took Adam and handed him over to the archangel Michael, saying to him, 'Take him up into Paradise, to the third heaven, and leave him there until that great and fearful day which I am about to establish for the world.' And the archangel Micahel took Adam and brought him away and left him, just as God told him at the pardoning of Adam" (Greek Life of Adam and Eve 37:4-6; written possibly in the middle of the first century AD).
"People who depart from this life in accordance with nature's law, thus repaying what God had lent them, when the giver wants to claim it back again, win everlasting fame ... their souls remain without blemish, and obedient, and receive the most holy place in heaven. From there, when the ages come round again, they come back to live again in holy bodies" (Josephus, Bellum Judaicum, 3.374; written in the late first century AD).
"And Abraham entered the depression of death. Death said to Abraham, 'Come, kiss my right hand, and may cheerfulness and life and strength come to you.' For Death deceived Abraham. And he kissed his hand and immediately his soul cleaved to the hand of Death. And immediately Michael the archangel stood beside him with multitudes of angels, and they bore his precious soul in their hands in divinely woven linen. And they tended the body of the righteous Abraham with divine ointments and perfumes until the third day after his death. And they buried him in the promised land at the oak of Mamre, while the angels escorted his precious soul and ascended into heaven singing the thrice-holy hymn to God, the master of all, and they set it down for the worship of the God and Father. And after great praise in song and glorification had been offered to the Lord, and when Abraham had worshipped, the undefiled voice of the God and Father came speaking thus: 'Take, then, my friend Abraham into Paradise, where there are the tents of my righteous ones and where the mansions of my holy ones, Isaac and Jacob, are in his bosom, where there is no toil, no grief, no moaning, but peace and exultation and endless life' " (Testament of Abraham 20:6-14; written in the late first century or early second century AD).
"The earth shall give up those who are asleep in it; and the chambers shall give up the souls which have been committed to them. And the Most High shall be revealed upon the seat of judgment and compassion shall pass away... righteous deeds shall awake and unrighteous deeds shall not sleep. Then the pit of torment shall appear and opposite it shall be the place of rest; and the furnace of Gehenna shall be disclosed and opposite it the Paradise of delight....Now this is the order of those who have kept the ways of the Most High when they shall be separated from their mortal body. During the time that they lived in it, they laboriously served the Most High and withstood danger every hour, that they might keep the Law of the Lawgiver perfectly...The fourth order, they understand the rest which they now enjoy, being gathered into their chambers and guarded by the angels in profound quiet, and the glory which awaits them in the last days. The fifth order, they rejoice that they have now escaped what is mortal and shall inherit what is to come ... the spacious liberty which they are to receive and enjoy in immortality. The sixth order, when it is whown to them how their face is to shine like the sun, and how they are to be made like the light of the stars, being incorruptible from then on" (4 Ezra 7:32-36, 88-97; written in the late first or early second century AD).
"When they, therefore, will see that those over whom they are exalted now will then be more exalted and glorified than they, then both these and those will be changed, into the splendor of angels and those into startling visions and horrible shapes...For they will live in the heights of that world and they will be like the angels and be equal to the stars. And they will be changed into any shape which they wished, from beauty to loveliness, and from light to the splendor of glory...And the excellence of the righteous will then be greater than that of the angels" (2 Baruch 51:2, 10-12; written in the late first century or early second century AD).
If you add in early Christian statements from the NT and the apostolic fathers, they fit in rather well to what has been presented above.