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Are you talking about the ambient temp switch underneath the freezer door? That doesn't affect the heating element at all. The only way the heating element should be getting hot is IF the main on/off switch is on and the fridge is plugged into a live AC outlet AND the board is getting a good 11 VDC current to it. IF the heating element is coming on WITHOUT the fridge being turned on, then the control board is defective and the heating element relay is stuck on. Even so, the fridge should cool depending on what the outside ambient temps are. If it is below freezing it will be harder to cool and at some point will be too cold outside to cool at all. Are you sure you got the correct heating element? They all look pretty much the same, but are different watts ratings, just like lightbulbs. If you put a lower rated heating element in there it won't develop enough heat for the fridge to work properly. The wattage is stamped into them up near where the wires take off. Those would be things to check. It is possible that the cooling unit may have a blockage or is starting to leak out coolant and not working well. If you hear any noise in the cooling unit when it is hot OR see any yellowish debris around the base of the flue area by the burner it is a sure sign of this and you would need to have a new or rebuilt cooling unit installed. Hope this proves helpful here. Please get back to me if you need more on this as all follow ups are included and fully expected.
I am attaching a copy of the Dometic Service Manual which covers this model so you can follow along on what I told you. Very helpful and you might want to print out a copy so you have it. I am also making a phone chat option available for you in case you want to discuss this with me over the phone. Some customers find that easier to understand or quicker on diagnosis questions. I should be around most of the day today. http://www.fourwheelcampers.com/NewDometicRefrigeratorManual.pdf