My Magic Chef refrigerator (Model# CTB2124ARB) suddenly started running NON-STOP. Both the freezer and the refrigerator compartments stay plenty cold, it just never stops running. The compressor feels warm but not hot, however there is frost on the tube/pipe that runs from the compressor into the back of the refrigerator. I've tried setting the controls to 1 (7 being the coldest) and it still runs. I've also tried turning the whole thing off for a couple hours and restarting - no change.

You have a bad t-stat it sounds like. You can get a universal replacement, but be careful to have the same length of capillary tubing exposed on new one as was on old one. Carefully coil up rest and tuck behind t-stat without bending sharply or touching any electrical connection. You should take in old one to refrigeration parts store to match it. Two wires plug onto it and it does not matter which one goes where. DrTom4444