Well, Bradley quickly sent me a new controller. It acts the same as the original one - 56 VAC on the jumper cable when the heat control is in the "OFF" position. I took a look-see inside and particularly at the heat controller. The multimeter argues that it is a variable resistor/potentiometer. And it is not a very high quality one at that; it builds resistance at an unsteady rate across its range. Anyway, the wiring disappears directly into a central control box, as does everything else. So, dunno.
BULL