Thanks for the tip on the potentiometer. I should have checked back here before finishing out the repair, but it may come in handy in the future.
The only dead component I found was a thermal fuse in the motor windings. I couldn't see any physical issues with windings or motor, and the bearings seemed to turn Ok, so I ordered a new thermal fuse of the appropriate rating and put everything back together.
While I was at it, I added some SAE20 oil to the resevoirs for the sintered brass bearings. Vornado claims the motors don't need service over their "lifetime." Maybe they've derated the motors enough that that's true over 10y or so, but the motors themselves have little pop-outs in the stamped sheetmetal housings to allow the addition of oil.
The front bearing is easy to reach just by taking off the grill and pulling off the molded fan blade. The back bearing is a hassle. You have to disassemble the motor to get to the fasteners that hold the motor housing to the fan to get at the oiling inlet. If you are doing that, it's easier just to leave the back of the housing in place and oil the pads from the exposed inside surface.
But enough about the mechanics, I just thought I'd add a helpful hint for anyone repairing a Vornado fan that comes across this thread. Everything works, for now. I did a full-speed test for an hour or so without I didn't notice any glitches as I swung through the range of the potentiometer.
I still don't know what caused the thing to overheat. There was a little bit of pet hair and dust flug in the path airflow takes through the motor housing, but seemingly not enough to cause a significant restriction. The bearings seemed to turn freely. I'd oiled them a few years ago, and while the felt resevoir pads looked a little depleted, they still had oil. Adding oil didn't cause an obvious reduction in resistance either.
I guess time will tell whether it goes for another several summers, or if it craps out again soon.
Thanks again for the help.