In The Name of the Rose, name and briefly describe the heresy that is explored during Days 3 and 4 and finally fully explained "After Compline" on Day 4.
The "heresy" is actually Adso's thoughts and reactions to his act of love with the peasant girl. This is something that has been dwelling on his mind since the event, and in particular he has been debating within himself whether what he did was good and pure or hopelessly depraved and evil. As Adso and William enter the library in the chapter highlighted in this question, Adso has the opportunity to search the pages of various texts to find the answers that he seeks about love, love-sickness and remedies. Although Adso finds many different ideas of how to become cured from love-sickness, it is clear that he finds no definite answers as to whether what he experienced with the girl can be definitively classed as a sin or not, as he still seems to be very confused about this issue:
And was the night I had spent perhaps not bestial and lustful? No, of course not, I told myself at once, it was most sweet--and then immediately added: No, you are wrong, Adso, it was an illusion of the Devil, it was most bestial, and if you sinned in being a beast you sin all the more now in refusing to acknowledge it.
The heresy of love and sex is thus examined, and Adso's confusion and feelings about what he is naturally drawn to and what his own conscience tells him is wrong is further highlighted. There is no clear answer that Adso can receive from the books that he and William find, and the text makes it clear that this is something that continues to trouble him.