That's good info, RegUS_PatOff! Since I was already in refrigerator-repair mode (and, my wife wouldn't mind), I checked all my existing thermistors to see if they were the old defective type so I could replace them before more stuff would go wrong.
As it turns out, all of my thermistors are the newer sealed and flat-topped style sensors. I even pulled the bad one out of the trash, and it was the newer style as well.
It looks like my Fresh Food evap thermistor just went out-of-spec. That probably doesn't happen very often. I guess it was my lucky day?