But hey, I probably destroyed my Norcold with my fancy wiring tricks- so be careful about getting too "tricky" (details below).
The "thermostat" definitely controls both AC and DC electric (poorly), using a low-quality temp sensor mounted on one of the cooling fins inside the Fridge. But for gas, the "temperature" dial itself constitutes the "pin" of a needle valve, and directly controls the volume of gas flow through the line (silver in color) which runs up from the TM gas connector to the dial and valve, and then runs back down to the burner.
It appears to me that the dial position is the ONLY control for flame size (excluding the "protection" shutoff, of course). I never saw any adjustment in flame size being done automatically by Norcold, according to temperature state in the fridge. Once turned on, the only adjustments were manual - I had to turn the dial down for late night and early morning, then turn it back up for afternoon heat. Dial "down" = flame size down; dial "up" = flame size up.
After my complicated "upgrade", My system allowed for a "Boondock mode":I would turn the switch to "Propane mode" and set a moderate flame size (i.e., dial position well below max) so that Propane would not freeze the lettuce at 5AM. Then I used a switched 12V power source,
external to the Norcold "Mode" switch, to run the DC electric heater via the PID thermostat (accurate to less than 1/2 degree). It would run as needed (more in the day, much less at night) to maintain constant temperature for in the fridge.
WARNING: It is possible that use of that technique, over time, damaged the ammonia mixture by applying too much heat for extended times on really hot days. With the PID controller set to try and maintain temps below 40F, even while ambient ballooned past 100F, the DC electric heater unit would run almost continuously. The Norcold design doesn't allow for more than 140 continuous Watts of power input, and my scheme would create that much from electric (whenever the PID controller decided that DC power should be added), plus whatever setting I had made for the gas burner (typically 80 Watts or so). But on the hottest of days, I would often turn the propane dial all the way up, creating 280 Watts of input power. That might have been a serious mistake
Per my sig, I have replaced it with a high-end compressor model. (That's a 12V compressor, not a "dormitory" fridge). And my new Fridge is
very famous for the problem under discussion here - going into unwanted "defrost mode" when the compressor doesn't run enough. (Due to lower-than-designed for ambient temps, combined with fairly good exterior insulation. Everyone says "it was built for the tropics").
As with Norcold, there's only one thermostat, and it's located in the Fridge section - paying no attention at all to freezer temps. In my case, insulating the freezer box from the warmer fridge section has been the main solution - they were previously separated by only the "freezer case", a box with
very thin plastic walls, providing virtually no insulation at all. Frequently opening the main fridge door to create "more demand" is less optimal, IMO.