Guys, here are some links. I would have to see your unit, but if you state the thermostat has no adjustments, just the P.C. board, one would think the dip switches would be on the board in the front A/C unit. I will look at these as well, but I have to ask, where is your thermostat mounted? If by a heat duct, consider the air from the furnace, (or A/C duct, same deal) This would give problems. Mine is mounte in the corner by my fireplace on my 3400RL. (A good location.)
Digital Thermostat change out instructions:
http://www.rverscorner.com/articles/hunterstat.htm
Rv Furnace troubleshooting;
http://www.ducktec.com/furnace-trouble-shooting.htm