Why can't I measure 240V on this wall heater wiring?
You say the thermostat is "Single Pole". I take that to mean that there is one wire in and one wire out? Does the wire out happen to be white? If so, the reason you don't have any voltage on the white wire at the heater is because your thermostat is off. Set the thermostat so that it turns on and test again.

Alternatively, test from the wire on the in side of the thermostat (which is probably white) to black or ground and you should get 120V.