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.