The fact that the OP mentioned a refrigerator switch (clearly not a PID) and no-one made any effort to tell him he could do better than a thermostat. We may have known but OP didn't.
Thank you for pointing this out. Sometimes it takes time for the members here to jump in and respond.
Just for your information, as you are new here, there is a huge reservoir of sous vide related discussions in this Forum on any topic you can think of. The posts must numbered well over a 100,000 including from many very well known authors and manufacturers.
Regarding switching refrigerators, many inexpensive aquarium temperature controllers can do that by incorporating a slight time delay for the refrigerant to equalize.
The Mellow circulator mentioned above will not need that because the cooling is done using a solid state Peltier device, not a mechanical compressor.