What are you using to stress the CPU to see if it's stable? You have to run something to keep the CPU usage at 100% to check for stability. Do a google search for Prime95 and run that for a while to see if it's stable...
Also using the computer will tell you if its stable or not. Play some games do a few other things. If its not stable you'll know. If it is then move up to the next level.
make sure you enter the password into prime95 in order to get the stress test. i believe it's 9876. run the stress for the maximim amount of time you'll use the computer in one sitting, then add an hour or 2.
max time in front of computer i.e. games, photoshopping: say 3 hours.