Did you try to clean out the fan?
Last year my computer kept crashing while I played high end games, just like you. I tried everything, right down to reformating. Right when I was about to give up, I noticed that the computer only crashed when it ran really hot, and it was some of the hottest days in summer.
A quick blow of canned air to the fan got out caked on dust. It turned out, the fan wasn't spinning nerely fast enough to do it.
Now with proper fan matinence, it doesn't crash at all.
Sometimes the simplest things are the way to go.