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I mean... The cooling parts of the smaller one outside of the big one so it doesn't heat it up.
Emmm, no.
The whole point of the fridge in the fridge is that the "cooling parts" (by wich I assume you mean the condenser, wich takes the thermal energy out of the compressed coolant) of the smaller fridge are in the bigger fridge. Because then the coolant will get even colder in it's condensed state, soo that when it expands it has even less thermal energy divided over the volume, making it even colder!
Need/ need no further explanaition, or should I just quit talking about fridges?
And just for the record. I know this because learning how cooling tech works is actually part of my college program, not because I spend my free time learning how fridges work...