I tried running my Dometic 2-way fridge on propane while traveling and here is the problem I ran into. I was going the speed limit (50 mph) in Glenwood Canyon and it was very windy as well. The wind apparently buffeted my propane flame which (I did not know it at the time) got a little frisky and caused the thermal fusible link near, but outside of the burner & chimney, to melt. This safety feature shuts down the fridge on propane totally. When I got to Grand Junction, I could not figure out why my fridge worked on AC but not on propane. Fortunately, I found a great mobile RV tech and he figured it out in a few minutes. The fusible link is close to, but like I said, outside of the burner, not in the chimney and it looks like a wire with a loose heat shrink on it. Inside that sleeve is a metal link that melts and breaks the circuit if the propane flame or exhaust should ever leave the confines of the burner or chimney. It looked just fine – no sign of burning – the melting point of the fuse must be quite low. I had no other indication of flames or heat outside of the burner. Lesson learned.
The RV tech gave me about 3 or 4 of them as spares. He was a licensed Dometic warranty repair man and had to retrofit the fusible links onto some older models, so he had extras. So now I carry the spares with me. And I know if I am at a windy camp site and my fridge on propane stops working, I will check that fusible link for continuity first thing.
We have never traveled with the fridge running on propane since. We use the ice box method. At the start of a trip, whatever space is in the freezer after frozen food is put in there, we fill it with blue ice and frozen water bottles. We also fill the fridge with cold water bottles, beer, wine, whatever will fit. When we will be on the road for the day we move a blue ice or two and a couple frozen water bottles out of the freezer into the fridge part. Everything stays cold. At night, back on propane, the blue ice goes back into the freezer and is refrozen by morning. No problem.