That's not a new problem that no one has dealt with before. The ISS for instance has its External Active Thermal Control System (EACTS).
It's not so much a matter of whether it's an unsolvable problem but more like, how expensive is it to solve this problem, what are its limitations, and does the project still makes economic sense once you factor all that in?
It's not so much a matter of whether it's an unsolvable problem but more like, how expensive is it to solve this problem, what are its limitations, and does the project still makes economic sense once you factor all that in?