I had a similar thermostat though my air conditioner is a heat pump model and replaced it with a Honeywell digital blue backlit model about a year ago. Overall it works well though the Honeywell has one annoying "safety" feature, the heat will not turn on if the interior temperature is below 32 degrees F. Apparently the theory is if an unoccupied house were to have a power outage in cold weather and freeze so that pipes break, it is better for the heat to stay off until the owners return. My planned solution to this design feature is to grab the hair dryer out of the bathroom and blow it on the thermostat for a few seconds if needed, thankfully it has not been needed yet. There are some youtube videos and web sites that will walk you through the process.
Note some of the youtube videos refer to wire color this is not a good way to do it, as different RV's may use different wiring color codes, even the same brand may change the color codes from unit to unit, instead label by function and move wires accordingly. There is a message thread on another forum where a guy is dealing with untangling the mess caused by assuming his rv used the same color code as a youtube video right now. For this it is smart to take a digital photo of the wiring on your old thermostat before you disconnect it.
See
https://www.youtube.com/watch?v=RFmyzGhHIgw
this setup is close to what I have, though the instructions are lacking, though I mounted the fan hi/low switch on the side of the plastic thermostat vs in the wall.
https://www.youtube.com/watch?v=6CPtV_iX9GQ