That has been covered to death since months, there is no good solution to cooling without an atmosphere. But even going into the technical details is a waste of time, think about how complicated maintaining such a system in space would be compared to having it on earth, the whole idea is a complete grift from beginning to end. There is literally no benefit to do it in space other than as a marketing tool.

Nobody who suggests the idea has ever presented a model that is even remotely close to reality