Why does the girl need ox heart to give her favours to the ugly monk?

It's not specifically an ox heart...it's just anything to eat.

The (translated) base novel explains

William “Very well, but we can deduce who it was from many and certain clues. First of all, the man was old and ugly, one with whom a girl does not go willingly, especially if she is beautiful, as you say, though it seems to me, my dear wolf cub, that you were prepared to find any food delicious.”

Adso “Why old and ugly?”

William “Because the girl didn’t go with him for love, but for a pack of scraps. Certainly she is a girl from the village who, perhaps not for the first time, grants her favors to some lustful monk so as to have something for her and her family to eat.”

^{The Name of the Rose - Umberto Eco}