Hi welcome to the forum,
I'd be prone to making a change similar to this:
RV Digital Thermostat Upgrade | ModMyRV
Often you can find a T-stat by Hunter etc. at your local home improvement center.
Another thing to keep in mind with hot weather is where the T-stat is mounted. They do best on interior walls, VS. a hot exterior wall that may have direct sunlight on it.
We know the insulation leaves something to be desired in RV's. Also, be sure the hole the wire protrudes through is plugged with insulation / foam etc. The blast of hot or cold air through it can mislead the sensor.
J & J
+ Kickr's the Vonderhund
, ES-38RSSA, 19.6K#
, 3500HD-Max, CC, 8'-DRW, 9.2K#