Presuming this refrigerator is out of warranty and you’re making diy repairs, what’s left to diagnose and troubleshoot are the refrigeration unit and timer. If the timer isn’t electronic and the typical electric clock with electrical contacts for motor and heater circuits, mark the timer and return an hour or more later to see that it turns. Troubleshooting worn electrical contacts would be the next step to check for pitting, preventing good electrical contact with intermittent operation of the heater. Timer and/or contacts may be a one piece part. If not a timer issue then the refrigeration unit may be worn out.
Refrigerators usually have two temperatures, the main refrigerator with around 40F to 50F and the icebox around -15F to 0F. My first guess with intermittent temperatures ranging wildly would be the timer being erratic. I would determine timer function, once or twice a day defrost and monitoring when defrost occurs over several days to be sure the timer isn’t slow from being worn out.