have you thought about hanging a dollar thermometer in the trailer, to take the reading?..... or go digital and get the 10 dollar model.
I purchased an indoor weather station for our trailer, but is really nothing more than an indoor/outdoor thermometer with automatic baro system that displays the most likely weather pattern we should see within the next 12 hours....
and as long as the cheap thermostat, that was installed at the factory, keeps cycling the furnace/AC on and off as it should, its a good working system.... usually the difference between a good operating t-stat, and one that doesnt allow for good heating/cooling of the area, is the anticipator setting may be wrong... its a bit harder to understand the importance of, and adjust the anticipator, but its what allows for even and efficient heating and cooling cycles. and all t-stats have the feature, but it may be called something else by that particular manufacture.