I purchased a used upright store cooling case with glass door (Turbo Air brand), equipped with a mechanical thermostat. The beauty of it is that this type of a thermostat usually has a calibrating screw, which can be used to tweak the internal temperature to the desired range.
As I turned the screw clockwise a few turns and the compressor went off. I left the fridge running for an hour to stabilize the temperature and then turned it back half a turn at a time, pausing for an hour each time and taking the internal temperature - until I got it to run at 52 F with the main adjustment dial in "normal" position at all times.
I'm not sure how easy it would be to do with a household fridge where parts are squeezed tight and access panels are not easily removed by unscrewing a few sheet metal screws but this is as cheap a solution as you can find.
