We've got one of the Peltier* ones, and my sister-in-law has one of the Sterling cycle ones. The Sterling cycle one doesn't self start, and needs to be flicked in the right direction once warm. The fan rotates slowly, and is metal to be heavy enough to act as a flywheel.
The Sterling one got dropped and stopped. Inside the big cylinder is a displacer that is held together with friction. Pushing it back together got it working. The materials are interesting. Aluminium displacer, full of holes and spirals of brass wire to be a regenerator. The piston is graphite running in a glass cylinder.
* The Peltier fans do not use the Peltier effect. They use the Seebeck effect, AKA thermoelectric effect. However, Peltier cells are made in quantity for coolboxes and the like, and can just as well be run in reverse to generate electricity from a heat difference rather than the other way round.