Phone not coming on

What happened prior to this issue? How did you discover this was going on? History could help rule stuff out since this could be any number of things. It certainly sounds like hardware. Where exactly on the back of the phone are you feeling heat? If you can narrow it down.

Mostly this sounds like there is a short circuit somewhere. I might check and see if it's recognized by a computer if it's plugged in via USB, but that seems unlikely given what you described.

This could be an issue with a part, (battery, display, etc....) or the board itself. I would either try to open it and see if you can narrow it down to a faulty part (unplug everything other than the bare essentials and try to power that way) or take it to a repair shop where they could do something similar. This could be as simple as a bad battery, but it's hard to know without getting in and taking a look since there is a long list of candidates.