Need help with Dometic Duo Therm Air Conditioner

I think the aluminum "wire" in your picture just to the right of the connector is your thermostat.

It monitors the temp of the air coming back into the AC and turns the compressor off when the temp reaches the setting of the knob.

If you turn the "colder/warmer" knob down (that is the thermostat) to minimum and the unit does not shut off after it cools the TC, then the thermostat is bad.

The unit can freeze up if the humidity is high and it isn't cutting off.