Thermoelectric cooler/generator to run fan

I’ve been interested in thermoelectronic devices for a while now, but they’ve just recently begun to be really inexpensive.  For instance, cheaply made Chinese units can be had on eBay for $1 each.  Each unit is rated for an output maximum of 2volts and 700ma.  Plan on getting half of that with room temp on one side of the unit and 300F on the other.  That means that an array of 12 of these little fellas could supply enough voltage and current to effectively run a 120mm computer case fan.  Put this in the doorway between a room with a woodstove and the adjacent room and you will start moving some serious heat!  The best thing about it is that the fan would only start running once the stove got up to temp and once the stove cooled down the fan would shut off too.