Both of the above posts have very good points. Put empty milk jugs full of water in there as you get room.
I've never heard that fridges run more efficiently b/c they have nothing to cool. Also what your talking about isn't necessarily efficiency of the fridge but cumulative demand (e.g. we're not talking about the mileage but rather the total distance driven). If the fridge were perfectly insulated and sealed, it would run only once each time you open the door to recover from the air changes. Because of physics in our macroscopic world this is impossible, and your refrigerator gains heat through conduction and infiltration. The idea is that convection (to items in fridge) and conduction (internal to each item) is a slower process than the air changes in your fridge. This allows for the significant energy rise to be absorbed my as much mass as possible (also reducing the total volume of air which can be exchanged) which results in only maybe ~1 or 2 degree temperature change as opposed to if your fridge was empty the temperature change would be much more significant.
This is why I like having my bottom freezer fridge with 2 half doors. I can open just the door that has pop behind it minimizing the air change in the space, as opposed to opening the full size door nearly all the way to get something that's near the hinge.
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