Apple was very adamant about not having fans, it wasn't until the Mac II and SE that any Apple computers had a fan. I think it was a Steve Jobs obsession.

Blown fuse is almost always a shorted chopper transistor. Nearly all switchmode power supplies have the same basic layout. Input->fuse->rectifier->bulk filter capacitor->chopper->transformer->rectifier->output filter. Look for a beefy 3 pin device on a heatsink near the big capacitor.

Shutting down after it's been on for a while is frequently a cracked solder joint or component drift causing either the output to drift up and trip the overvolt shutdown, or the shutdown circuitry to drift and falsely trip.