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Making my bet before watching it: It has to be the toaster because of the semi-enclosed design coupled with the insane output from the heating elements. The toast will rapidly cool once popped, but it will still be toast.

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In general it seems to me that heating stuff is way simpler and quicker than freezing stuff. There must be some scientific explanation because I can not claim to know it. So yea my bets are on the toaster too

That's the second law of thermodynamics. Heat flows freely from hotter places to colder places, but getting in to flow out of somewhere so it gets colder than its surroundings requires some trickery

Energy cannot be created or destroyed. The toaster changes energy from the electrical grid into heat, the fridge can only move it from inside the freezer to outside the freezer. Making heat is much easier, but it ultimately depends on how fast each of them can work.

Fridges use half the amount of power as a toaster, but fridges run at 150-250% efficiency (1 amp in is 2 amps of cooling) it can even be as high as 400% in some conditions. This means given the same amount of power, a freezer would win. But it depends on how much each appliance can actually use.