Phone dead

I am guessing heat can only come from discharging the battery in a non-intentional way. Short circuit or something internal.

Did you plug it into something besides the connector it came with?
An FM transmitter for the iPod killed mine.
Hard reset, wall charging, USB charge, iTunes restore, replaced the battery ... still dead.
Considering how hot it gets, (could be a fire hazard?) surprised Apple doesn't issue a notice or warning.

Caveat emptor, going back to Motorola.