Verified answer

It's the other way around. It moves heat from the box into the freezer.

The problem is that the box isn't very hot, so heat will flow very slowly from it into the freezer. If the box isn't very well insulated, then heat from the room will flow in just as fast when it's only a tiny bit cooler.

Otherwise, you'd need something like cooling coils, and you force a chilled liquid through the coils. That gives a lot more area for heat in the box to be absorbed.

Passive heat flow in your case is going to be too slow to make much of a difference.

You cannot transfer "coolness". You are mistaking it with a transfer of heat, a form of energy. For example, when you get colder, it's not because coldness is entering into you; rather it is heat leaving your body.

Going back to the original question, to make a efficient passive transfer of heat from the box to the freezer, you will need two type of material: either a conductive inner material, and an outer insulator enclosing the system. The conductor makes the transfer of heat easy, while the insulator makes sure that the only heat reaching the fridge is from the box. Look up on google for items that have a high specific heat for you insulator, and the reverse for your conductor.

On a side note, I do NOT advise you do this to a freezer. It kind of kills the fridge by decreasing its shelf-life through overworking it, and your food products will suffer for it.

There is a thing called a heat pipe that conducts heat very rapidly (which is what you are actually doing here). It's basically a sealed copper tube with some volatile liquid inside. Heat evaporates the liquid and the vapour travels along the tube, condenses at the other end and releases the heat.

They are fairly expensive I think but you might find some on ebay.