This is indeed the main reason, but for FFs there is the point mentioned about where the stat is located.It is freezers which play up (possibly also F/Fs). And it's not because of where the thermostat is, it's because they stop working when the ambient air gets too cold.
Actually, it's not hit and miss at all - it gives pretty good control of both fridge and freezer temps within certain limits. See below ...Its fridge-freezers that play up. Reason- there is only 1 compressor and 1 thermostat on a fridge-freezer and the thermostat is in the fridge bit. Which has always seemed a bit guess and go to me but hey......
Actually it does closely control the freezer temp provided that the fridge is needing some cooling. Allow me to explain ...Is that not probably because it's more important to maintain the fridge at the appropriate temp (not too warm, and certainly not sub-zero) than it is to maintain the freezer at a precise temp?
As you will be aware, for any given pressure, the boiling point of a liquid will be fixed. So by controlling carefully the evaporator pressure, you can control it's temperature - and you can control the evaporator pressure by the system and compressor design. In a FF, there are two evaporators - one in the fridge and one in the freezer, with the liquid refrigerant being passed through the freezer section first.
So, as long as the fridge is calling for some cooling, the freezer will cool to the temperature fixed by the refrigerant cycle design. When the freezer is cold enough, the refrigerant will stop boiling off and will then get carried over to the evaporator in the fridge section and cool the fridge. In effect, the freezer gets "first bite of the cherry" and only when it's cold enough does the fridge get some cooling. When the fridge section si cold enough, it's stat turns off the compressor. This works fine as long as there is some heat leakage into the fridge - but in very cold weather I can confirm "by experimental results" that the demand on the fridge stops being sufficient to ensure that the freezer gets to stay cold.
I did actually consider how to make a fridge or freezer for the Land Rover given that a V8 is not renowned for it's frugality in sipping the go juice IIRC I once worked out that it could take getting on for 1kW to vapourise the propane*, and by setting up a "pre engine bay" pressure reducer I could get a fairly effective little ice box. I was actually thinking of either a liquid circuit to an "in car" cabinet, or probably more practical, a small box for freezing ice packs to then use ina cool box.
* It sure as heck froze the reducer very hard if there wasn't sufficient circulation (eg airlock). At atmospheric pressure, propane boils at -40˚, and during maintenance work I have had the opportunity to look into a partly filled tank with some liquid propane bubbling away and hoar frost rapidly encrusting the outside.
... and yes, -40˚ is cold enough to cause some rather painful "burns".