Power supplies can fail for a variety of reasons including excessive temperature. One lesson I've learned is to always check the cheap stuff first. Some people, when confronted with a problem, simply start swapping out parts until they finally get things to work again. However, that can get pretty expensive if you end up buying parts you don't need.

Be careful about opening your power supply. Many of them were really designed as throw away units because they aren't worth repairing. If your unit can be opened, be sure to do it safely. Not only must you unplug the unit (Hey, people get shot while cleaning firearms, so sometimes it doesn't hurt to state the obvious. No offense intended.), but you need to watch out for the capacitors* in the power supply. Some of them can hold a charge for a long time even after the unit has been unplugged, so stay away from the terminals.

If you can swap out the fan with an old one, go for it. If that doesn't work, you can turn on the power supply and wait to see if it goes out again when hot. Replacing the power supply usually isn't too expensive, so I wouldn't wait too long before replacing it if you're sure it's bad. Sometimes, a dying power supply can send out voltage spikes that can damage computer chips like the CPU or RAM. Silicon will burn out far faster than a fuse ("silicon will blow to protect the fuse" is an old electronics technician saying).

* Back in 1976-77, I went through Avionics Technician training. My instructor was an old retired Navy tech who told us a funny story about discharging power supply capacitors. It seems that his old instructor was teaching them how to work on a mobile RADAR unit that was mounted in a metal van. He said, "The first thing you have to do is discharge the capacitors. You do that by shorting across the terminals with a screwdriver." As he demonstrated the step, he didn't notice that he had one finger on the screwdriver blade. The capacitor was huge, and when it discharged, an electrical arc shot about a foot between the man's butt and the metal walls of the van. It burnt a hole in his pants, and he wasn't at all amused by all the laughter.