Have you run the Apple hardware test? I think its on the install CDs, boot up holding down the 'D' button. Might give you an idea as to what the issue is.
Next, I would run it in single-user mode (Command+S on restart) to see if it goes crazy doing something as basic and simple as that. If so, you'll know it's not a software issue.
Boot up on an external HD (perhaps the internal HD is buggy - who knows)
If you have extra RAM Modules, take one out and run a basic system and see if it heats up (RAM issues?)
Run with no brightness or an an external screen to see if running the backlight is heating it up.
Clear up some HD space, though I've never heard of this making the computer over heat, it may help with sluggish processing.
Take out battery/power cord and hold down power switch for 8 seconds.
Zap PRAM (Command+Option+P+R on reboot).
Obviously, test without any peripherals (mouse, keyboard, etc.)
Hope some of this helps - Good Luck.