One obvious question: does this remote thermostat actually control the furnace at all, or is it just for the AC or something?
Maybe it has some sort of a minimum temperature that can't be overridden, though I can't say I've encountered such a thing myself. Maybe either the remote thermostat or another one can cause the furnace to come on. Maybe mice or abrasion have caused a short in the thermostat wiring.
Maybe, if you're like me on my less glorious days, you mistake the water heater for the furnace. :W (I don't know that I've actually done that, truth be told, but I quite firmly believe I could.)