The material you describe would still just be moving the heat around. Both the material itself and the current it generates will both have heat. No matter what you do with the heat it will still be there, making things all hot.
You could get rid of excess heat by throwing hot things into space, but that is just another type of radiator.
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The longer answer involves getting into a physics lecture. Heat has a lot of rules that are very well understood, and it is more reasonable to think FTL travel is possible in our lifetimes than it is to think that heat transfer can be cheated. Rule number 1 of heat is that heat can not be created or destroyed. Rule number 2 of heat is that temperatures will always try and equalize. If you put a hot thing and a cold thing next to each other you'll end up with two things of equal temperatures.
So you can't just transfer all the heat off Yamatai into a cube and blast that cube into space because your lukewarm yamatai won't transfer heat into anything warmer than it.
Nor can you convert that heat into mass without also making that mass very hot, so hot that you won't be able to put the heat from your luke warm Yamatai into your now super-heated cube once you've made a cube using Aether.
But what if you were to take a bunch of ice-cubes and launch them into space? Well, you'd still cool down the planet! Those ice cubes still have heat in them, heat that is now leaving the planet. Now there is less heat in Yamatai per square foot, and that heat will all spread out, lowering the overall temperature... but we don't want to send all of Yamatai into space just to get rid of a little heat.