The problem with going by colors is that the coach maker installed those colors- not Dometic, so they may not cross over, but you can look at the ceiling assembly to see what colors come out of the control box, and wire accordingly.
That said- *if* the black is ground, it's correct, otherwise green should be ground.
If the control box is OK, twisting all wires other than white and red together will give you high fan cool- if it does, the problem is in the thermostat, if not, the problem is wiring, control box, or power to the control box (12 volt or 120 volt).
But- Dometic has had a bunch of thermostats, all of which operate differently. Knowing which thermostat would help.... a lot.