Is the computer
Beeping or
Buzzing from inside the case before it shuts down? I would try trouble-shooting with the ram chips first before anything else. Pull them out...run with one in the #1 slot.....then run the other in the #3 slot. Then try running with one chip in the #2 slot then adding the other in the #4th slot. This is to see if one of the ram chips are faulty. There are memory tester programs out there...I just can't think of any right now....I am sure one of the
build your own Guru's will post one or two of them on here.
Also try this with the extra fan blowing on the inside of your case....
Some computers like Dell's have LED lights on the back of the case that tell if something is wrong too. My Dell has 4 LED's that when everything is ok they are all green.
It does sound like a heat problem....or at least your computer is protecting it's self by shutting down.
EDIT: One thing I always do is to go to
www.pcpitstop.com then run the tests there. You have to download an Active X file...then run the test...takes about 5-10 mins depending on your connection.