The modern understanding of atheism and agnosticism wouldn't have truly applied in the middle ages. There are examples of critics of religion, but the conception of doubting the existence of a high creator wasn't the same as we understand now.

In middle ages Islam, some scientific scholars criticized the role of religion and dogma. One example of this is Abu Bakr al-Razi. He was physician, alchemist and philosopher who view of the metaphysical did not create a creator type God.

In middle age Europe, to my knowledge, there is no specific expression of atheism. However, there was counter-dialog to documents such as Thomas Aquinas' five proofs of God. These efforts to counter these premises were not to support atheism, but were to support the premise that belief in God was innate, in support of their need to be happy.

There were charges of atheism, used as a political attack. One example of this is Pope Boniface VIII, who posthumously was accused of being an atheist. Edit - typo

As an aside, Dante wrote that Atheists went to the First circle (Limbo) a nebulous place, where, because they didn't believe in God, God didn't believe in them, and so were not in Hell, but not in Heaven.

It is not outside the realm of possibility that the Holy Roman Emperor Frederick II was an atheist or an agnostic, but it's hard to separate polemic from reality here. This is the sole notable example that has any sort of credibility.

Of course common knowledge says that they would immediately be burned at the stake, but I think it's likely to be more complicated than that.

Common knowledge is wrong. There actually relatively few burnings at the stake. Unless this atheist was actively preaching atheism it's doubtful that he or she would even be noticed, and if they somehow were, they would be asked to repent their heresy (for it would be considered heresy), before being excommunicated and possibly turned over to the secular arm for a more physical punishment. Private belief was between you and God; so long as you weren't endangering the rest of the flock, your damnation was your own business.

For the record, I know of no such prosecutions.

/u/Agent_Peach said:

However, there was counter-dialog to documents such as Thomas Aquinas' five proofs of God.

Of more note - Aquinas' theology didn't really come into full application until the Council of Trent in 1555 - was St. Anselm of Canterbury's so-called (by Kant) Ontological Proof of the existence of God, an argument designed to convince any rational person of the existence of the Divine.

This sort of proof is not an attempt to counter a rash of atheism. Rather, it was proof-of-concept of Anselm's creed of faith: credo ut intellegam - I believe so that I might understand. Believing in God, Anselm went about attempting to understand that belief.