Unless you have heat pump rooftop A/C units, then your furnace is separate.  It sounds like your thermostat is not getting the signal from the furnace, indicating to me a disconnect between the furnace unit and the thermostat. My furnace is located underneath the refrigerator unit and has an outside access door.  Since I have not had any problems with mine, I have not poked around in there, but I suspect there may be a fuse or disconnect or fuel valve or something in that area that may be a problem.  
If you look on the outside of the coach, you should see an access door similar to that of the water heater (mine is on the passenger's side underneath the refrigerator access door).  I'd start there and trace access to the furnace components looking for loose/damaged wires, fuses, connectors, etc.