Is there anything you can do with a fan in the fridge to better circulate the cold air?
In my experience, it is important to ensure that there is no, or little ice buildup on the cooling fins in the fridge compartment. The ice usually builds up o the RHS of the fridge where the coolant enters after it has circulated through the freezer compartment.
Now, this side of the cooling fins is also where the thermostat is clipped to the fins.
Once ice builds up around this area it severely interferes with the ability of the thermostat to then regulate the fridge temperature.
In my fridge ice buildup usual y happens after around 6-7 days. But it will depend on the humidity of the air and especially how often the fridge door is opened.
I have a very small battery powered personal fan which I place on the RHS under the cooling fins immediately after lunch when the ambient is high and thus the fridge has filled with warm outside air. It takes a couple of hours for this to melt the ice, get the fridge regulating correctly, and bring the temperature down. I remove the fan when I next open the fridge.
I have not needed to have a internal fan running continuously. But I note that many people including
@Boots in Action have one permanenyly mounted, running continuously and have had good results from doing so.