It is certainly possible that you have a bad thermostat. But first, are you sure that the door gasket is good, and that the door is tightly closed? As I recall, it is possible to close the door "a little bit", leaving the gasket not quite seated. This situation would result in bouncy temps, although I would expect it to be warmer than you are seeing. And how about the freezer door? Is the spring in good shape, meaning that it closes firmly? If it flops out against ther inside of the refrig door, then all sorts of strange things may happen.
The refrig must be more or less level, but precise levelling is overhyped. If you are comfortable walking on the floor (i.e., you don't stagger like a drunk due to the tilted floor), then the refrig is happy.
On propane, I don't think the flame size will change as you move the thermostat. The flame itself is either on or off - when you move the control to COLDER, the flame will simply stay on longer. But the on/off cycle isn't very fast - you might have to watch for an hour to see a difference.
Somehow, though, I wasn't aware that you can actually see the flame without disassembling something. Is there maybe a bunch of insulation missing, especially in the area of the "heat tube" (for want of a better name)? This is a vertically-oriented sheet metal tube in the back of the refrig - all three heaters are inside it, and it is pretty well insulated with fiberglass insulation.
Finally, what is the model number of your Dometic unit? Do you have a manual for it?
Bill
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