I suppose the answer to this question depends on how you define "closely." "The Last Temptation of Christ" movie is based on a book by the same name written by Nikos Kazantzakis. The book represents the author's view of Christ after decades spent following other leaders and teachers from history and religion. The book was controversial when it was published, and Martin Scorses's film adaptation of it is just as controversial. Your question asks whether the Jesus portrayed in the film is close to Jesus in the Bible, I would have to answer no.
Certain key events in the movie-Jesus's life are factually accurate. He is the son of Mary and Joseph, he lives in Nazareth, he has followers, he teaches and performs miracles, and he dies on the cross. It is the specific portrayals of his character as well as outright biblical inaccuracies which make Jesus something other than the Jesus of the Bible.
The most disturbing difference for me is the idea presented in the film that Jesus did not know the plan for his life before he arrived on earth. In fact, according to the movie God only reveals it to him, rather bit by bit as Jesus lives his life. Note the following dialogue between Judas and Jesus from the movie:
Judas: If you're the Messiah, why do you have to die?
Jesus: Listen, at first, I didn't understand myself...
Judas: No, you listen. Every day, you have a different plan. First it's love, then the ax, and now you have to die. What good could that do?
Jesus: God only talks to me a little at a time and tells me as much as I need to know.
Judas: We need you alive!
Jesus: Now I finally understand! All my life-all my life, I've been followed by voices, by footsteps, by shadows. And do you know what that shadow is? The cross. I have to die on the cross, and I have to die willingly.
Contrast this idea of an uninformed and rather befuddled Jesus with the Jesus presented in John 1:1-3.
In the beginning was the Word, and the Word was with God, and the Word was God. He was with God in the beginning. Through him all things were made; without him nothing was made that has been made.
Jesus is the Word made flesh, and it is clear that there were no surprises for Jesus. He knew from the beginning of time what the plan of redemption would be.
Another disturbing inaccuracy in this movie (at least for those who are followers of the biblical Christ) is Jesus's distortion of the concept of Divine Judgment. When Jesus teaches through parables in the movie, no one is ever condemned. Lazarus (Luke 16) gets to leave hell and the foolish virgins (Matthew 25) get to attend the wedding. This may look like mercy from a kind-hearted and benevolent Christ, but the effect of this teaching is that God is no longer a keeper of His word, and that is a foundational doctrine of the Bible: what God says, He will do. If that is not true, God is not true.
There are many other elements in the movie which depict a less-than-biblical Jesus. Kazantzakis created a Jesus who was more human than God; so when Jesus the man-god made the choice to withstand temptations and finally to die willingly on the cross, the sacrifice looked greater, in his view. The Biblical view of Jesus is even more stunning in its sacrifice, for it depicts a Jesus who, from the beginning of all creation, knew he was going to have to be the atonement, the price which had to be paid for giving humans free will and the right to choose good or evil. Knowing that, he still came.