Depending on the MP3 Player the problem might be different, but if you are dealing with a Li-ion battery the over heating might be a sign of battery failure. This failure maybe causing the protection circuit to trip and stop power production. These failure are sometimes brought on by water getting into the battery and shorting it out. So if you dropped it into water, or where is a very wet area that might be the problem.
I would seggest replaceing the battery, or goto a battery shop that deals only in batteries and see if they have one that try out and see if that fixes your problem.
Sorry about the bad luck.
-Bill
Bill, March 2006