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R -----/\/\/\---|>|----- W
... perhaps a high value resistor in series with an LED .... it is possibe that a small amount of current could pass without activating the heater ... the LED would actually be emitter part of an optocoupler ... when the heater is off, the LED is on ... the thermostat contacts short out the LED when they close, which causes the LED to turn offHeater on → 0 (shorted)
Heater off → 17Mohm
I hope I hooked it up correctly to Arduino to detect it.