It sounds like an overheating issue. When you play a game, it taxes your computer which causes it to heat up. Go through your computer and check all the fans to ensure that they are working and also make sure that nothing around your computer is hampering the air flow from any exhaust fans. Don't forget to check the fan on your video card (if it has one) to ensure that's working too.
You might also want to take this opportunity (since you'll have your case apart while inspecting your fans) to take a can of air and clean your case and components. Dust will hinder cooling fans, causing them to spin slower than normal which could cause overheating.
Hope this helps, let us know if it doesn't!
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