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Lumifer comments on Stupid questions thread, October 2015 - Less Wrong Discussion
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Sure, but I don't see a problem here. If you have a particular attachment to a star system, you may want to supply it with energy from other stars instead of moving to them.
The point is that since the energy will get "consumed" elsewhere, the waste heat at the origin will be minimal and so the Dyson sphere will remain relatively cold (though higher than the background temperature, to be sure).
However, the destination star would emit large amounts of heat, i.e., infrared.