(I don't have background in physics so apologize if this is a silly question)
(I don't have background in physics so apologize if this is a silly question)
You could actively cool the planet in principle, of course; but to do anything noticeable, you'd have to operate on geographical scales. You'd probably be better off building towers to the edge of the atmosphere and putting infrared radiators like this on top of those; otherwise, the your best bet would be to replace a few million square kilometres of a hot region with black paint and make sure there are never any clouds overhead.
That would be counterproductive since black would absorb more of the sun's energy during the day than it would radiate at night. What you'd need is a way to have a black surface during the night and white during the day. (But barring that, white all the time is better than nothing, because it reflects more of the incoming sunlight. This is why melting of polar ice caps can accelerate climate change.)
All that being said, this is not in and of itself a climate change solution in the way you might be imagining. Most surfaces on Earth are effective at radiating heat already, and do so (it's in climate models). The difference here is we're thinking about actively making use of the cooling effect from a device, or building-scale to offset energy uses.