Does the image of Jesus in The Last Temptation of Christ (1988, Martin Scorsese) follow the Bible closely?
This is a difficult question to answer because the writers of the Gospels use a style that is not dramatic nor emotional. Compare the Gospels with Paul's writings, for example, the Letter to the Romans, in which Paul starts and interrupts trains of thought, perhaps to pick up the train of thought later, perhaps not, and exudes excited emotion and passion. Further, the Gospel writers use a style of narrative in which the stylistics switch from past tense to present tense in mid discussion.
This style does two things: (1) it gives an immediate sense of place and action and (2) it produces a dream-like quality, a spell-like quality. What this all means is that the Gospel writers were endeavoring to present a case for the facts they were presenting and were attempting to use traditional narrative style to achieve a particular sense of presence in time. As a result, the Gospels are not focused on presenting an "image" of Jesus; they are focused on presenting a reality of Jesus, a presence, a sense, if you will, of the fact of Jesus.
What this means in reference to your question about The Last Temptation of Christ (1988, Martin Scorsese) is that any "image" of Jesus that is not dream-like and ethereal, if you will, must be from Scorsese's creative imagination based on the events Jesus lived rather than on the "image" of his personality created in the Gospels (the Gospel of John is the one that differs and adds some dramatic and emotional imaging but only in the service of enforcing John's point of the divine attributes of Jesus: Bread of Life, Living Water, Eternal Life etc).
American Standard Version (ASV)
35 Jesus said unto them. I am the Bread of Life: he that cometh to me shall not hunger,...
Having said this we can ask: Does the image of Jesus in the film match Jesus' participation in events and present a fair interpretation of that person who would have done those things in those events, e.g., throwing the money changers from the porch of the Temple? The answer to this question is, yes, the Jesus presented in the film is fairly represented as participating in the events told about and matches with the person who would have done what he is said to have done in those events.