No No, did I really write this? Silly thought, as it would be if I mentioned about leaving it in a sunny spot. Not much help to you at all, I know, but I'm also intrigued by what could possibly be the reason for the iPad getting hot if you haven't used it before putting it in your briefcase.
The frustrating thing is that there must be an answer. I hope you will find it Mr. Davey. Admiral Adama's suggestion seems the only course of action now.