Lets talk about heat real quick....
Heat can't be created or destroyed. It has to come from somewhere and it will stick around if you don't get rid of it.
In Yamatai's case, it is taking a little bit of heat from the Aether Universe and bringing it to Yamatai. This lowers the temperature of the Aether universe by a little bit, and raises the temperature in our Aether generator a whole lot!
Now, we can use that heat to do work. We can turn it into mass, use it to move space ships, heat homes, ect, but regardless of what we do with it on Yamatai that heat is still on Yamatai. We can push the heat around a bit if you like, but you're really just taking one big hot spot and spreading it out so that you raise the temperature across Yamatai by a small amount. Eventually, if we keep using this heat to make mass or otherwise do work Yamatai will have so much heat sitting around from the Aether universe that it will cook the planet.
Now before you go and say "Why don't we just send it back to the Aether?" Remember that heat can only go from high to low. If we open up a hole to the Aether universe we're going to get the much hotter universe pouring out into our much colder universe. Luckily we have something very big and very cold nearby: Space. Heat naturally radiates away from a planet, and all that heat that has built up on Yamatai will naturally radiate out into space. Over time the very warm Yamatai will lose heat out into the very cold space through radiation. If you turn off the sun and the Aether then Yamatai will quickly freeze due to this heat loss. The problem with global warming is that carbon traps heat on the planet and prevents it from leaving, since Aether doesn't release carbon then we aren't in danger of Yamatai isn't really in danger of burning.
Of course, if we do need to get rid of more heat there are ways we can do it. The best way is to let that heat beam out into space and for that we need radiators. A good radiator would be a large white surface that can reflect heat away as well as let it radiate off the surface and into space.... a large, flat, white/grey surface would also be a great place to land starships too...