Brian, those things are a royal pain in the arse. MOST of the time it's not the controller under the cabinet in the kitchen area - generally its the wall control unit. I think i've replaced a dozen this year so far, exact symptoms. I even had one that even though it was switched OFF on the front unit, it would randomly light the furnace.. hehe. You can check your temp sensors mounted in the walls with an ohm meter... I don't remember the exact resistance, however it you heat it with a hair dryer you can watch the readings change with heat/cold. Remove the wall control panel and disconnect the wall mounted sensors wiring before testing ohms - otherwise you'll get false readings generated from the wall unit. I don't think I've ever had a wall mounted sensor fail - but if you do it will either show open or shorted regardless of the temps you throw at it.
94-Newmar Kountry Star 40-KSDP
Spartan/Cummins 8.3C-300HP/Allison 3060 WTEC-II/25yr RV Tech RVIA Certified/Onan-Cummins Certified