Heat, memory and power are the most likely culprits. I lean more toward power though.
First, check your wall outlet. Are you getting good power? If you can, test it. Do you have other devices drawing power on that circuit?
You can try moving the computer to another wall outlet on a different circuit as well. Too many devices sucking juice from the circuit will cause a power "sag" and can make your computer restart.
If all this checks out, it's time to be suspicious of your power supply in the computer. Is it under-powered for your system? Most computers should run with a 300W supply nowadays.
Is the power supply itself starting to fail? This does happen. If you have a volt-ohm metre try measuring the leads from the power supply to see if you are getting 3.3V, 5V and 12V (within a 10% tolerance range).
Some motherboards allow you to check the temperature of your processor. After a reboot, go into the CMOS and see what the temperature is. If it is above 55 degrees, heat is the primary suspect.
Finally, to troubleshoot memory, try removing all the sticks except one. Try this stick in different slots. If the system seems stable, shut it down and start adding memory back in. This won't work with Rambus memory though as you must insert it in pairs.