Problem with iPod Touch randomly rebooting.

My Itouch is acting strange. It will reboot randomly. I found that if I am using wifi and playing a game, it will reboot automatically.. while using Facebook it's fine. It will reboot when it is connected to I-tunes, sometimes fine, but I have to try to update it a few times because it will reboot before it finishes (with an IoS update).. The ipod works better with wifi and bluetooth off, it does reboot if I skip a number of songs...

I think it may be tripping the overheat signal, so it reboots. However... the device is not hot. A coworker told me a new battery could fix this? Is this true?