There is a thing to cool the processor of the cpu. But it only cools one side. It transfers heat to one direction. But you can say it cooling..
Cooler paste or a heat sink does not cool an object due to electricity but because the material leads heat away from an object being heated by electricity. There is no current running through cooler paste.
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Re: cooling
I don't think there is any mineral/material/substance on Earth that will "decrease in temperature as electricity runs through it". But if you find one I'm sure you'll win a Nobel Prize .