If it is a Dometic brand. The first thing to test is the Thermistor. That is what the probe is called that is attached to the fins inside your frig. You do this by opening up the panel on the outside of your camoer where the fridge is and take the cover off of your circuit board. Find the wire harness which is usually on the upper left, disconnect it and attach an ohm meter to the two prongs. Set it to read resistance and then go back inside the camper, slide the plastic bracket holding the thermistor off the fins and dunk the probe in a large glass of icewater. Go back outside and watch the meter to see what the thermistor is reading for resistance. If it is out of range as mine was, you have found the problem. This is the usual fix for a overcool problem. If the thermistor is in the normal range, it is your circuit board. I recommend the Dinosaur brand of circuit board if you need it.
The man that runs this business is T.J. Gillmore and is the best person in the country for parts, great service and a fantastic website with a forum to ask questions in. Look up your model number frig for troubleshooting specs and parts.
T.J. will respond to any question you have. I know this because I had the same overcool problem you have with a Dometic 2652 that didn't have a temp dial either and I fixed it for $24.00 with T.J.'s help.
You will have to cut the harness plug off by the circuit board on the two wires for the thermistor, Tape the end of the new Thermistor to these wires and have a friend help you by pulling the wires inside the camper as you feed them up the back of the frig from the outside to replace the part. It's not hard to do.
Good luck and PM me if you are still having trouble.