I've found cheap after-market thermostats to have short lifetimes... Original lasted 20 years... Replacement started misbehaving in just 2 years.
So now my policy is to retrofit all old refrigerators with digital STC-1000 thermostats. A bit more work to cut out some plastic, split the hot wire and tap into a neutral wire (easy enough to follow the bulb) but cheaper, super reliable, and gives very consistent and highly controllable results.
Two such upgraded refrigerators are still working without an issue several years later. Though both required replacing the relay (with a solid state relay/capacitor unit) at about the same time, and one after replacement of the evaporator fan motor due to noise issues.
Electrically, you just need to: 1) connect both wires from the old mechanical thermostat to the "Cooling" terminal block (polarity doesn't matter). Or if your model doesn't have separate heat/cool the "relay" and configure settings for cooling mode rather than heating. 2) Tap into hot and neutral wires (going to the light bulb but BEFORE the door switch) and connect that to the STC-1000 power input (polarity doesn't matter).
Then configure the STC-1000, set a temperature to maybe 4C and set the "compressor delay" to at least 4 min, though I'm happy with 10. The default difference of 3C should be fine.
The plastic cutting varies by refrigerator design, but shouldn't be too confusing.
So now my policy is to retrofit all old refrigerators with digital STC-1000 thermostats. A bit more work to cut out some plastic, split the hot wire and tap into a neutral wire (easy enough to follow the bulb) but cheaper, super reliable, and gives very consistent and highly controllable results.
Two such upgraded refrigerators are still working without an issue several years later. Though both required replacing the relay (with a solid state relay/capacitor unit) at about the same time, and one after replacement of the evaporator fan motor due to noise issues.