@paulraphael Is basically correct. I would explain it a little differently.
If we assume the fridge is well insulated, the major heat gain would be from convection when the door is opened.
You open the door and cold air flows out and warm air flows in.
If I have just one bottle of water in the fridge the temperature change from the warm air would be more than one bottle of water can absorb.
If you have a couple of cases of water and open the door for the same amount of time, the water can absorb much of the heat
with out a major change in temperature.
Ether way the fridge needs to expel the additional heat. It just might not need to cycle on as often with the larger mass.
There seems to me to be a secondary effect of reduced air flow if the fridge is full.