Kenmore 564 freezes on Min setting

Hi -
I recently took a Kenmore mini fridge (564) out of storage and found that it is now freezing things even on min temp. Have tried on both max and min settings for 24 hours each but both settings will freeze a cup of water on top shelf. Temp knob appears to be working as I can hear the fridge turn off / on when turning knob to off position. Unit is maybe 5-7 years old. Not sure what it is but there’s a little round sensor, indicator, or light just below the temp knob inside the fridge. If it is a light, it’s not lighting up. Don’t have manual anymore and would appreciate any help!

Thanks.

It looks like most parts for your unit “Requires special attention” at AppliancepartsPros but they may still be able to get them.
You would have to call them.

I would say that it is a thermostat problem.
The off is a mechanical setting and just because that works it does not mean that the thermostat will regulate the temperature.

I was able to find that the Sears part number for the thermostat is 301917.

Awesome! Thanks, I’ll give that a try.