Whirlpool Side by Side cools down but stops?

I have a side by side Whirlpool refer ED20TK. It will run, but after getting to the desired coldness, the motor/compressor shuts off. All is normal, except it will not come back on unless I change the temperature to warmer & then colder. Only then will the thing start to run again. This repeats itself. Don't want to spend $150 toi have it repairred if it is just a tempostat that I can replace myself. Any ideas what could be wrong?

Paul in Seattle
August 18 2007