pilots are entitled to refuse an aircraft anytime...whether it's an MEL'able item or not. anything to do with APU or pack u/s should automatically be refused because of the uncomfortable work environment it creates for us. anything that causes physical discomfort is a distraction and is a safety concern.
i'm sure you've all experienced the cockpit temperature never dropping below 38C. try throwing in a couple of major abnormals inflight and see how well you perform under those conditions!!