I had a customer audit once where the guy argued with me that SQF requires me to monitor the employee fridge temp, said he was going to write it up in his audit that we weren't SQF compliant when I argued. I stuck to my guns, three separate SQF auditors prior hadn't required it of us and that code makes no explicit mention that the refrigerator must be monitored. We responded to his "finding" that we were compliant with SQF code on the matter and would take his observation under advisement. In the end, I did post a sign that stated employees should tell a supervisor if the refrigerator stops working and updated our breakroom policy to reflect employees should report a non-functional refrigerator.
Refrigerator was only for employees and the company did not provide any foodstuffs inside it, and it could be that second part where an auditor is upping their attention to the matter. If the company is providing some of the food in there, especially say overrun from production products for employees to have, then arguably it's a finished goods refrigerator now too and subject to monitoring.
Temp wise, should you decide it needs to be monitored: if keeping company provided stuffs, it should probably be checked daily and kept under the max temp for your finished goods. If only keeping employees bringing their lunch foods, I'd honestly look to see what the maximum temperature setting of the refrigerator is and say someone should notify a supervisor if the temp exceeds that maximum. I'd happily argue employees themselves are checking it each time they grab their own food, and the reporting of it non-functional is captured by them at that time.