This is pretty major, probably hasn't happened to anyone else or they would've posted.
Well anyways, i used to get this problem on my ipod where it would stop working randomly, i just rebooted it and it'll start working again. This sometimes takes more than one try.
The fact that the phone was warm may also have burned circuits? I don't know but that's very odd since you weren't using it. Ask google, i'm just shooting in the dark