PSU getting very hot, system turns off after 20 min
My PS3 fat (CECHE01) is overheating somewhere. If I run it for a while, the internal fan gradually increase in speed, and the PSU gets extremely hot to the touch (can't leave my palm or fingers on it for more than a second). Eventually it turns itself off, and the red light doesn't come on. If I leave it unplugged from the wall for about 5 minutes, I hear a click from the PSU, and then I can turn it on again. If I have fan blowing on it, it doesn't overheat (used it for about 6 straight hours last night with a fan, and had no issues).
Is this a power supply issue, or is the overheating coming from further within the PS3, and the power supply is just conducting the heat?
Any help is appreciated, thank you all in advance.