1. The wall tstat will NOT cause short cycling
2. You HAD to have miswired the new Tstat
3. Some RV makers use the 2- FURNACE 12 volt wires that go to the Tstat to POWER the tstat.
4. Now for some fun with you. I don't know what engine I have in my car but it is located beneath the hood, Hope that helps:B
5. Really need brand and model of furnace. Because some models have a 12 volt circuit breaker that will trip if you shorted those wires when replacing the wall tstat. Can you reinstall the original wall tstat, if you remember or wrote down the wire color codes? Doug