The reefer should do better than the 37* they got it to. At the top of the refer, on the coldest setting, it should just about freeze things.
A fan inside would help, but it should also work without it. Remember the cold radiates(?) down from the freezer fins. If the refer is packed too tight, the cold can't work it's way downward. There's no natural air circulation in there.
They do make replacement adjustable thermistors that work better than the original, but again, new from the factory, it should work correctly.
Go buy a cheap remote thermometer with at least two remotes so you can put on in the refer and one in the freezer. You loose a lot of cold checking it all of the time. And, you'll know what it's doing while driving down the road.
If you want to pay little more, by a thermometer that registers four sensors. Refer, freeze, inside RV temp and outside temp.
Bill