|Where and how did you check the temperatures? If you checked in the BIOS that is at system idle. Under load the temps can go up. |
If you are using Vista tools to check the memory it may not to a thorough job.
Download memtest86 and run it from a boot disk run the full program. Takes more than one hour, depending on the amount of RAM.
Desktop computers get pretty dusty inside the case. Open it up and look. Use canned or compressed air to blow it out. DO NOT use a vacuum cleaner. Will be messy, may want to move to a different location to blow.
While you are in the case you may as well re-seat all the cables, cards and memory. Snap the RAM stick in and out 4 or 5 times each to burnish the contacts.
All the above is good maintenance. If the computer still shuts down then install a temperature monitor like Speedfan to see if the temps are the problem or not.