My kenmore refridge shuts off. I unplug it for 2 hrs and it starts. It last about a day then it shuts off again. Could it be my temp control thermastat?

When you say "shuts off". What exactly are you meaning? Most refridgerators turn off and on as needed to cool the unit.

Check the temperature in the freezer and the refrigerator with a good thermometer. Adjust the temperature control and allow 24 hours for the temp. to stabilize. Temp. should be in the 35 to 40 degree range.
Just noting when you hear it start up or stop doesn't tell us anything.
What is the temp. after it has been shut off for two hours? If you don't know, you may be eating food which can cause you harm.

Check to see if the coils are dirty. It sounds like either the coils under the unit are clogged with dirt or the condenser fan is bad or dirty, or both are dirty and not moving air through the coils. Wash out the coils with spray soap and a water hose nozzle. That's the only good way to clean them. Make sure to clean the fan blades, too.