I need to know if your wall tstat looks like this? Doug
https://www.dometic.com/en-us/outdoor/climate-and-comfort/air-conditioners/air-conditioner-accessories/dometic-ct-single-zone-thermostat-164511The reason is simple. Even tho your RV is 2009, years ago Dometic had thousands of single Zone tstats that had a SIMPLE fault. If the interior of the RV was over 95 degrees, then the tstat failed to function. The only fix was a new updated Tstat which removed the heat failure problem. A way to test this was to take a PC air can, turn upside down and spray the cold on the tstat for a few seconds. If the Tstat and system functioned the tstat was your problem.