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The thermostat is just a simple switch on/off. Is it that the furnace doesn't run enough or does it over heat the house? You never really said in your first post what the problem is exactly.

It sounds as if something was jumpered out in the past. Just as long as none of the safeties where removed it should be fine. I don't know why the voltage would be 50% high, I see 22-30 VAC all the...