I have a dometic three-way and it has been rare that it has ever been too cold, but I would wait until you hit some real heat before making any changes or repairs.
I also run it on 12 volt when I am driving. But if I were to leave it on 12 volt it would draw down my Coach batteries in a matter of hours. Mine is also a newer model which has an automatic power selection. If 110 is available, it runs on 110. If not, it looks for propane, if no propane it goes to 12 volt. When I am traveling I manually switch it to propane if I am stopping for lunch or more than just an hour. It also has a safety feature where it will not run on propane for 10 to 15 minutes after the engine has been turned off. This is to prevent having an open flame while you might be refueling your vehicle.
One last point, I have added auxiliary fans, a small pair inside the fridge, circulate the cold air, and four larger computer fans create a forced air flow Tru the void behind the fridge. The inside the fridge fan runs all the time, but the fans for the void space are run on a thermostat attached to the fridge coil. These are very low draw so they do not impact my power usage.