It might be your battery. It is semi-normal for the hard drive based iPods to get warm when charging and syncing them as power is being sent to the battery (causing heat) and the hard drives are spinning also causing more heat. The only things that can produce heat on the iPod touch are its battery and its display. The display can produce a very small amount of heat and the battery should only produce heat when it is charging but this heat is very small as well. So for one thing, it could be over charging the battery and that's not good.
But at first I try this comment from the Apple Store: plug the iPod into the USB-port, press and hold the "Select" button and just click on play at the same time, until the "Disk Mode" screen comes on, and then download the newest software (Firmware - You can download it at Apple's website), and update the iPod. See if that makes a difference. After that I would consider a new battery because it is a relative easy, inexpensive fix. You are not using your iPod while charging, and your backlight is off,right?