Can I install two thermostats to control one furnace?

Ok, thanks all for your quick responses. Wa8yxm thanks for your inputs, I went and checked the wires going to the furnace, there are actually 5 wires in there. A 12 volt, two white and two grey. I disconnected a white wire that controls the furnace, if this one is disconnected, the heat and eventually the fan will stop after all the heat is dissipated. There is another white wire that controls the heat only, if I disconnect the second one, the fan only runs but not the heat.

So, I installed a bi-metal T=stat in series with the white wire that controls the furnace On/Off. Actually cut the white wire and connect it to the new T stat, one end to one screw of the T stat, the other to the other screw.

Now, for Room heat, I put the living room furnace switch on and at full heat. I then put the switch ON on the room T Stat witch will make the continuity but only if the temperature lever on this new T stat calls for heat. When the room temp reach the room T stat preset, it cuts the power to the furnace. The furnace finishes it's cycle and shuts off.

For living room heat, I keep the room T stat ON and at full heat, and the living room T stat ON, but this time, the living room T stat has the controls, it will shutt off the furnace once the living room is at temp.

Looks like it will work? The grey wires, I do not know what they are used for but If I disconnect them, the furnace completely stops, fan and heat, so I do not touch these ones.

Any advices?

We set the t/s in the living area to 65 F at night and close down the only adjustable heating vent, which we have in the bedroom, almost all the way at night. That way the Living area gets heated up and the bedroom stays cool. In the morning we set the t/s up to 68 F. The vent can be adjusted to change the bedroom temperature at any time.
We also frequently have an electric heater in the living area to help maintain the temperature without using propane.
This is way simpler than trying to hook up two t/s.

On his Monaco coach he probably has the Comfort Control Center with covers furnace heat and the AC/heat pump units. If he has two AC units, it probably already has two temperature sensors that are fighting each other.

You can do it, Furnace control is normally two blue wires, You need a bi-metal or electronic T-Stat (I suggest the bi-metal type) NOT a mercury bulb type.

You will also need a "Front/rear" switch, a SPDT switch will do it,

Disconnect ONE of the wires from the existing T-Stat, run this one to the switch, Run a short jumper from the switch to the T-Stat

Run much longer wires from the other T-Stat furnace terminal and the other switch terminal to the bedroom T-Stat, Flip the switch for Day/night modes.

NOTE: This assumes the T-Stat ONLY controls the furnace, if it also controls the Air Conditioner you will have to find the needed wires. That can take a bit of searching.

If the thermostats are wired in parallel they should both work. You would need to set the temp very low on the one you're not using for the moment or switch it to off if it has that option.

You not only would need a second thermostat, you would need a switch to turn one on and the other one off. The wiring would be sort of a nightmare.
Of course if you do not heat the living room, it may get too cold and then warming it up in the morning would probably use up any propane that you saved during the night.
Use an electric blanket and maybe a small electric heater in the bedroom and turn the living room temp down a little bit at night.

We have two thermostats and only 1 furnace. We never have both turned on for the furnace - reason being, the furnace would run almost constantly between the two locations calling for heat and when it does run, heat comes thru every vent anyway just like it does with only 1 turned on. What are you trying to accomplish by having 2 hooked up? If you want to bump it up from in bed in the morning before getting up to let it warm a bit first, that would work as long as you later turned 1 of them off.