I use automotive paint from ppg, everything i have done has not had an issue. It is rated for 450 degrees, and if the bay gets hotter than that, you need not worry about the paint.
Rat, i wish i was closer, but sonce i am not i have a question. The doors, i have that almost cardboard stuff, my question is what do you use in place of that when one needs replacing, and where can i get it?