My suggestion would be to turn on the furnace, and let the camper warm up, allowing enought time for for temperature sensitive items to warm up. Then, once you start towing the camper, it will be much less likely to cause and splitting or breakage of plastic or vinyl components. While the furnace is running, open up all cabinet doors. And for such a shot haul, I'd leave the heater with thermostat set at 50 degrees or so if you know the furnace is operating properly. Traveling with the furnace on is probably as controversial as travelling with the fridge running on propane. Im not an expert....refer to your owners manual for any manufacturer guidelines re traveling with the furnace turned on.
If you are worried about it, then just get everything really warmed up, then shut down the furnace and tow the unit home.
