I had a similar problem like yours. PC would shut off only during gaming sessions. Temperature monitoring software showed that nothing was overheating. Power supply (not a cheap one either!) was still under warranty so I replaced it. That didn't help either.

The culprit turned out to be a bad stick of RAM. If you have multiple sticks, take one out. Play the game for a while and see if the problem persists. If it still does, put that one back in and take out the other(s) and repeat. It seems like my problem was a much rarer occurrence than having a Power supply failing, or overheating... but hey, it happened to me.