Air conditioner issues

assuming you want to heat to cut off below 50 degrees

what makes you think the T-stat is faulty

what is the RV inside temp, 50, 60 , 49 ?

the heat is not going to come on until the stat is set above room temp

is the RV only 30-40 degrees and you want 45 degrees ?

you have not given enough info

heat pump or LP furnace

So the sensor is on the main unit and not the tstat?

Sounds like you have an analog or mechanical thermostat. You could upgrade that to a home style digital. Google for or check mod my rv. To use the Domestic digital you would have to upgrade the control box. The Dometic thermostat works fine for some and terrible for others having inconsistent temp control which was one of my problems with it. Don't suggest Domestic digital for an upgrade.

Only numbers I see is 310762-008. Actually on the card.
Another is 0952, that's a sticker.

Need to know what Dometic tstat you have. They make about 8 different models. Doug