I've run isopropyl alcohol in an ultrasonic cleaner.

It did get significantly hot after a while. And smelly, so it was surely aerosoling (is that a word?) somewhat.

I did it outdoors and away from anything that could catch fire because it felt rightly sketchy.

It's basically an industrial ultrasonic humidifier attached to the bottom of a buffet tray. And it does get warm.

A lot of ultrasonic cleaners have a heating element.

Typically not (though some have heaters you can apply) but they atomize the fluid pretty well. The tiniest spark (static electricity) and some bad luck and you have the lid shooting into the roof and then a fire. As with everything, if you know what you are doing, go ahead.