You are hoping to keep the fridge running with solar so you don't have to worry. That depends on the scenario.
We tried it with the TC we had and 300w of solar flat on roof and with a 3.2 cu ft Igloo 120v fridge. We had four batteries by putting some in the truck box in front of the wheel wells and ran wires into the camper from them. Anyway it was a nail-biter whether it would all keep going four or five days with solar helping out.
It would not work on battery alone. The fridge ate AH. Some solar was enough to keep the batts over 50% before going home. Sunny every day was good.
As it turned out, too many times there was not enough solar. We got a propane fridge in there as soon as one showed up in the "used" ads.
That is why the one 310w panel might not be enough for what you want to do. It all depends on the scenario as usual.
BTW watch out what size MPPT controller you buy. EG a 20 amp Tracer will be too small. They have watts limits to go with their amps ratings. IMO a 40 amp Tracer would do it for sure and then some to allow for more wattage up there if needed and you can fit it on the roof. (There are portable panel options too that can be added to whatever is on the roof for more total solar.)
1. 1991 Oakland 28DB Class C
on Ford E350-460-7.5 Gas EFI
Photo in Profile
2. 1991 Bighorn 9.5ft Truck Camper on 2003 Chev 2500HD 6.0 Gas
See Profile for Electronic set-ups for 1. and 2.