I bought an analog fridge thermometer and an alarming digital thermometer. The defrost cycle would set the alarm off but the analog thermometer would not move

I bought an analog fridge thermometer and an alarming digital thermometer. The defrost cycle would set the alarm off but the analog thermometer would not move above ~40F So once it alarmed I watched the analog thermometer go up above 45F and stay there for hours. The back of the fridge was freezing over and preventing the fridge from working correctly. I bought the repair kit from the recall / service bulletin a couple years ago so that bought me a year or so of continued use.