As a late night cab driver, if you're ever wondering why I'm on the street rather than the driveway in your sketchy, pickup truck filled suburban neighborhood, this is why.
Give me a shady looking industrial district or run down residential neighborhood over semi-rural suburbia any day of the week. I feel much safer.
Heat doesn't go up. Hot air rises because it's less dense than cold air. You know what's less dense than hot air though? Vacuum. That's a good thing, though, because we don't want to be hemorrhaging atmosphere.
Even if we could build a physical heat sink sticking out of the atmosphere somehow, it would be less protected from solar radiation than anything inside the atmosphere, so if it were facing the sun it probably wouldn't work.
Even if we had the resources and like, enough readily available materials on Earth to make some sort of retractable heat sink sticking out of the night-side of the planet, it'd probably require more energy consumption to create than would be worth it.
Probably the best way to cool things down is to quit burning so much shit and quit knocking forests down.