It turns out that the fan was indeed bad. The problem is that there's no way to mount the fan in the case in the field. There are non-removable parts that get in the way, and the only repair is to replace the entire case. This meant that the tech had to rebuild the machine in the new case. The insides of the machine show Apple's attention to good design, aside from a couple of miscues (the non-field-replacable fan being the biggest). Overall, I was impressed. I was just as impressed that the $300 or so I spent on the AppleCare package has now been repaid; I doubt I could have had the guy come to my house twice for that, never mind the spare parts.
It's nice and quiet and cool again. I can't ask for anything more.