Well, the outside piping is supposed to get hot, actually very hot at the bottom. But the burnt smell is not a good sign. Can you see any indication of a melted wire anywhere?
I guess I would try the 12v mode, to see if the "burnt insulation" smell was coming from the 110 side. However, Very little of the wiring is actually 110, so its not likely to be isolated like that.
Does it also have an LP gas mode?
You can download the Service Tips manual for your Dometic RM2553 here:
Dometic RM2553 Refrigerator Service Tips manual