-3G iPod 20GB w/dock
-Newest update on the iPod
-Same problem throughout multiple installs, computers and iTunes versions
-iPod sometimes stops responding and gets really hot
Is there anything I can do or do I need a new iPod?
Try verifying and maybe repairing the iPod's disk with Disk Utility in the Utilities folder. Also try using a different cable and Firewire port. Unfortunately, I doubt this'll help though.
I would definitely try a different firewire port or use the USB cable provided. For months, my iPod would not be recognized by any firewire and only with my USB cable then it started working again.