Fridge not running, turns back on when reset. help!

We have a side by side Kenmore that has recently been acting up. Both the refrigerator and freezer will warm up completely until you unplug the fridge and then turn the thermostat all the way to off, plug the fridge back in and turn the thermostat back on. Sometimes it works if you just turn the thermostat off and on. The compressor will come on and run several times, usually working for about 18ish hours before not turning on again and everything warms back up. I have replaced the start relay and that did not do the trick. Any ideas where to look next?

Thanks so much!!

Here are your parts
http://www.appliancepartspros.com/parts-for-model-kenmore-10659028991.html

If you go to the Sears parts site they have actual parts breakdowns.
Unfortunately they do not share these with other vendors

Since you can get it running by turning the main control thermostat that is what I would replace.
Odds are that it is sticking open.
This is fairly common.
AP3037004
Click on the picture for more info.

Be sure to place the sensing wire back in the plastic sleave and the same position as the original.