I have the same model and problem. In my case it was the thermostat. I diagnosed it by bypassing it (connecting the wires directly to the heater vs through the thermostat) and turning dial on the timer on the lower front of the refrig under the grill until it went into a defrost cycle. If the heater goes on, it is the thermostat. I actually took the thermostat apart and repaired it. The solder was very poor and the unit had filled with water and froze which forced the wires to separate. A good re-solder and fill with RTV did the job. I wouldn't doubt that they all have this problem, even the replacements.
Steve S
February 2006