I have seen film curl badly if put in an overheated drying cabinet...
I've seen TriX that was left for *days* in a mildly heated drying cabinet. It wasn't curly, that would be an understatement. It curled both vertically and horizontally. Actually 3 pairs of hands were needed to make a contact print
Hi. This is what I learnt in a news darkroom many years ago. We used to dry the plastic base of the film with good quality chamois leather. Make sure you get all the drops off, because you only get drying marks on the plastic base. You don't touch the emulsion side at all as you won't get drying marks on the emulsion. Using a drying cupboard is not necessary unless you are in a hurry.
Probably not a good idea! It would, I think, be far too easy to damage film that way, either through excess heat or physical damage from the pressure itself if the platen has any slight irregularity. The reverse curling method mentioned in previous posts (either on a reel or some other cylindrical form) will handle the problem almost all the time. Just give it time to work!