So I know nothing about Dometic thermostats, but did a “bit” of reading on the enclosed links (that can be dangerous). So apparently Dometic analog thermostats use a different control box in the air conditioning ceiling plenum than their digital thermostats, so if you go digital TStat the digital control box must be used (if I read things correctly). The Dometic digital thermostats use three wires only and you can get capacitive touch, LCD or bluetooth enabled thermostats which all use the same three wire connection.Some interesting reading if my links work.....
New Dometic Thermostat Changeout - Forest River Forums
HOW-TO: Dometic analog to digital thermostat replacement (pic heavy) - Forest River Forums
So chadh, you probably have seen the links above already. You say you have a Dometic analog thermostat, but no control box in the air conditioner ceiling plenum at all.......what do the analog thermostat control wires terminate on then I wonder? Dometic TS controlling a replacement non Dometic AC unit maybe? If you have an older coach perhaps a previous owner did some changes?
As you say perhaps the control box is in the roof unit.......but that would be surprising (less weather tolerant situation up there). What I would suggest is that you obtain your air conditioning unit model and serial number (check your coach build sheet....should be posted somewhere in a cabinet or bedroom closet) and contact Dometic tech support to find out what gives? Let us know what they say......we non Dometic AC types can learn something here perhaps. Good luck.