Temperature readings don't always tell you if there is an extreme heat issue in an unknown spot. And of course, since you stated the computer shuts down "without warning", I'll guess you can't monitor the temp at the time it shuts down.
Have you checked the game sites to see if there are any updates for the games you're playing.. If there are such updates, give them a try.
The first thing we do here is to remove the case cover, then use compressed air to blow out all the dust from around the processor, heat sink, power supply, and all vents and fans.. Next, make sure all the fans are functioning.. Next, we remove the old thermal paste on the heat sink and replace it with a thin covering of new.
And if that doesn't get it done, it's entirely possible your power supply is either inadequate or heading south.. Time to swap in a new/bigger/better one.
Hope this helps.
My computer has recently had this problem where whenever I try and play graphicly intense games it shuts down without warning. My specs are:
AMD Athlon 64 2X 5000+
NVIDIA GeFORCE GTX 460
chipset: Geforce 7025
Southbridge : nForce 630a
motherboard : ASUSTeK Computer inc
any other spec i should include please tell me i really need help i can't do anything to shake this its not my temps because i monitor those when it shuts off and they are in beetween 55-65 C ive run countless scans with am\lmost every antivirus software to no avail