I run into this all the time up here on the mechanical style systems. Frigidaire even sells a 'garage' kit. There is no temperature sensor in the freezer, the knob for the freezer only controls a damper between the fridge and the freezer. If it is cold, the fridge doesn't get warm enough to turn on the compressor, and with a mechanical timer every 8 to 10 hours the defrost cycle still runs and warms the evap. coils up to where the thermostat stops it (40 to 50 degrees F). Eventually the freezer thaws and the fridge stays cool. Putting the fridge where it won't get below 40 usually solves the problem.
The Frigidaire kit simply adds a heater (I think it is 4 watts) around the oil bulb for the temperature sensor that comes on when the defrost cycle runs to insure that the compressor turns back on after the defrost cycle finishes. I keep one in stock.