|From your description of the problem it does seem that the computer is overheating, especially if:|
It makes less noise than it used to do (a fan which has stopped working would account for that).
It happens mostly when playing games (playing games is especially resource-intensive which generates more heat than normal use).
A visual investigation is required to confirm whether or not a fan has "died" and needs replacing.
If it's a PC, it may also need a thorough clean-out with a compressed air can to shift all the accumulated dust and dirt which prevents efficient cooling and, in really bad cases, can even stop a fan working.
If it's a laptop, likewise make sure all the external vents are clear.