Without some further info about the previous remotes and the new one, I don't think we can even guess. The furnace doesn't know or care where the heat demand signal comes from - it's just a "thermostat wire" that goes to +12v when heating is needed.
There must be a thermostat somewhere to monitor interior temperature for both heating and cooling, and that may communicate to the a/c zone controller. Presumably your old remotes operated that. Does your new remote do any of the needed functions, e.g. set temperature, select cool vs heat, fan mode, etc?
Former owner of 2004 American Tradition and several other RVs
Home is West Palm Beach, FL