On our last weekend camp out, it got cold both nights. The first night, the furnace worked fine. The second night, the RV got down to 50 inside because the furnace didn't turn on. When I got up the next morning. I tapped the thermostat firmly 3 or 4 times with the soft side of my fist. I heard a click, and the furnace turned on. The next week, I installed a new thermostat.
Please note that after installing the thermostat, testing the furnace will work. Testing the A/C requires that you remember to turn the 120v power back on first. (I spent about 20 minutes cussing and troubleshooting why the darned A/C now wouldn't work.)