I'm not sure whether you have a High Wall a-frame or standard. The way the fridges operate are different between the 2. The standard a-frame has a continuous run fridge with no thermostat or automatic relight on propane. The following is for a standard a-frame:
1) you have to run the fridge at least 12 hours before traveling to get it pre-cooled. I plug my a-frame in to a standard socket using an adapter, and turn on the fridge to "9" coldest setting on AC. This also charges my battery before the trip.
2) Many pop-ups (a-frame or tent) struggle to keep the fridge working on propane while being towed because the exhaust is in the side of the camper, not the roof. And they don't relight themselves (except some high wall models).
3) The technique that works best for these pop-ups (a-frame or tent) is to pre-cool the fridge, switch to DC while being towed, then switch to AC or propane at the campsite. The DC cooling is usually weaker than the AC or propane, so it will only hold the fridge, not cool it any further.
4) Upon arrival, I set the propane or AC to max cool for the 1st 12 hours or so. The next morning, if stuff is starting to freeze, I back off the cooling to "7". Check cooling about every 12 - 24 hours and adjust.
There are easy mods to make these small fridges cool more efficiently. Some are pretty good as they are, some need the mods to cool enough in hot weather.
just my experiences
now 2014 Rockwood A122 a-frame
then 2000 Coleman Westlake PUP