They run off piezo electric current Peltier Generator wherein the heat source needs to get hot enough to stress the materials which create the electricity required for operation (https://en.wikipedia.org/wiki/Piezoelectricity) (https://en.wikipedia.org/wiki/Thermoelectric_generator). There are wires that run from the solid material layer into the fan engine to power it, which then runs until the heat source cools down and it automatically shuts off (due to lack of heat power). The fans are relatively cheap too, I got mine on Amazon for like $40 and it works great and looks good as well. The main benefit is that they push the hot air off the top of the hear source (hot air rises) so instead of that air immediately going up to the ceiling it goes out in the room first before rising eventually. Mine usually kicks on when the surface it's touching reaches about 200 degrees and will run continually for as long as I keep my stove above that temperature. In case you want one, here's the one I bought off Amazon (https://www.amazon.com/gp/product/B01CD2AIV8/)
A nice 'luxury' item to add to the buddy heater is one of those wood stove fans that's powered by black magic, I mean heat.
https://www.amazon.com/VODA-4-Blade-Fireplace-Increases-Friendly/dp/B01CD2AIV8
These heaters are great but you can really stretch their heating power if you circulate that air.
That is a really good idea. Were you referring to something like this: