This sounds good, except that cooling a box is problematic. He needs the temperature sensor to read low so that it turns on the heat.
That said, if he has access to the interior of the thermostat, I'm sure it won't be difficult to replace the temperature sensor with a circuit to cause it to read either really high or really low on demand.
I was literally imagining duck-taping one of those cheap electric "instant cooling" cups over the box on the wall, and running a small incandescent bulb in to be the heating up element.
That said, if he has access to the interior of the thermostat, I'm sure it won't be difficult to replace the temperature sensor with a circuit to cause it to read either really high or really low on demand.