[Christ]

The thermostat only blocks flow to the radiator. It comes after the pump, and after the flow through the engine block. If the thermostat is closed, the coolant recircs through the block, then back through the water pump.

If the thermostat is open, the coolant proceeds through the water pump, through the block, through the thermostat, then into the radiator, and back to the water pump.

Because the circuit is built the way it is, you're looking at it backwards. The thermostat is a restriction to pressurized hot fluid, and doesn't contact the cooled fluid returning from the radiator to the water pump.

Therefore, instead of choking off the input of the hair dryer, as you suggested, you'd have to test the theory by blocking the output of the dryer (or box fan), which does actually place a load on it, because it's trying to compress a fluid. (Air, in this case.)