I have seen these fans in a couple of places and have now found out a bit more about how they work. They have no battery - just a metal base made of two different types of metal. This acts like a thermocouple. Thermal conduction results in movement of charge carriers, concentrating them in one place and resulting in a potential difference.
https://en.wikipedia.org/wiki/Thermoelectric_generator I notice that it is best when high electrical conductivity is coupled with low thermal conductivity. It seems to be the reversal of the Peltier effect, where running current through a two metal junction results in heating or cooling.
