daf bit: Gittin 81

According to a mishna on today's daf, if a man writes a get (bill of divorce) for his wife and then changes his mind, Beit Shammai says he has disqualified her for marriage to a kohein (priest). (A kohein cannot marry a divorced woman. I assume that we are talking here about the case where they stay married and she becomes a widow; according to Shammai she has some divorce-related impairment by the mere act of the get having been written.) Beit Hillel, on the other hand, says that even if he actually gave her the get, if it was conditional on some event that did not occur, so they were never divorced, she can freely marry a kohein (again, presumably after he dies).

The next mishna (also on this daf) says: if a man divorced his wife and then they are seen staying together in an inn, Beit Shammai says that she does not require a second get from him (i.e. we do not worry that they re-consumated the marriage) while Beit Hillel says she does require it. Both are talking, the mishna says, about the case where they were married; if they were only betrothed (which does still require a get to dissolve), then Beit Hillel agrees that she does not need it because he would not take liberties with her in that situation. (81a)

So it seems that Beit Hillel holds that if they were married (and then divorced) he will not resist the opportunity to have relations with her (which can effect a marriage), while if they were only engaged (and then divorced) he can control himself. The reasoning is not given.