To what extent do you think that the character of Dr. Faustus stands as a Renaissance hero?

Perhaps the greatest statement of Renaissance humanism occurs in Pico della Mirandola's "Oration on the Dignity of Man." The Neo-Platonic Pico emphasized human achievement and the importance of human's pursuit of knowledge. The Oration claims that through the exercise of the intellect, humans can ascend or descend the chain of being, and that this intellectual capacity, coupled with free will, makes humanity the most wondrous of creatures. Transferred to more tangible circumstances, Pico's "dignified man" can become Marlowe's "over reacher."
At the beginning of Marlowe's play, we see that Dr. Faustus is a person of middling birth who has improved himself though studies. He is superior in philosophy, law, and medicine. He seems to have "plumbed the depth" of human learning and seeks more. He has accomplished marvels in human terms and seeks to ascend to a level comparable to the metaphysical. This approach to human intelligence and the longing for more is a quintessential Renaissance desire. Even when we consider what necromancy offers him, we find that what he ends up accomplishing through Mephistopheles' help is exactly what the Renaissance was already offering (cheap theatrical tricks in conjuring ancient figures, getting food out of season by traveling to another part of the earth, pranking the Pope and undercutting his dignity).
Of course, Faustus fails to understand his reading of the Bible in the first scene, largely because he picks and chooses passages too carelessly, and thus fails to see the coherence in divine writ. In the end, he suffers the tragedy of a medieval man, and the medieval "psychomachia" or soul war represented by the good and bad angel, confirms that his end will be as grim as a medieval sinner would expect.

Doctor Faustus is a Renaissance hero in that he wants to develop his abilities to their fullest extent. Possessed with a firm belief in man's almost limitless potential, Faustus wants to push back the boundaries of what human beings are capable of, especially in relation to the acquisition of knowledge.
Yet Faustus's seemingly boundless confidence soon turns to despair as he realizes his own—and by extension, man's—limitations. Like all human beings, his reach greatly exceeds his grasp; he wants something he ultimately cannot have. Faustus's despair leads him to conclude a diabolical bargain with Lucifer, to whom he agrees to sell his soul; this is the only way he can achieve the kind of knowledge—and the power that goes with it—that he so desperately craves.
Faustus may be a Renaissance hero, but he also stands as a salutary warning against the kind of intellectual hubris to which the rediscovery of ancient learning frequently led.