How do you turn on the AC if not via the thermostat?
I have a Dometic single zone LCD, so they are available. I can't attest to replacing an RV thermostat, but my home unit was really easy. I labeled the wires before I disconnected them from the old unit, then matched them up on the new unit. But if you can't control your AC from your old unit, a digital thermometer won't help you unless you can find the wires that do control your AC.
I'm done. This isn't a place to be helpful. It's a place where curmudgeons with a superiority complex will nit pick everything. If you want help, go elsewhere. Admin, delete my account please.