It is risky to wire a commercial unit to anything that could inadvertently send current into it and ruin it. (Despite the care you take to think you're simply switching in a resistor). You might get the modification to work for you, but will the next owner of the house know what to do with it? And how to fix it?
I followed a clever hint to turn a plain mercury switch thermostat into a programmable type. I mounted a 7W light bulb to the wall below it. An ordinary plug-in timer turned the bulb on. Heated air rose up to the thermostat to 'fool' it. It stayed off during the night although room air went down to 60 or 65 degrees.
I guess that won't create the same effect you want.
Here is a way to achieve some degree of isolation. Suppose you were install a CdS photoresistor? Use your thermometer circuit to light an led at the needed temperatures. It will reduce the CdS sensor resistance. A lot of experimentation may be needed.