Heat doesn't "really" get trapped by greenhouse gases.
The earth is constantly heated by the sun's light (light hits the air, heats the air; it hits the ground, it heats the ground) and it's constantly radiating heat away (the ground emits infrared and cools down). The hotter something is, the faster it emits heat, so based on the amount of incoming heat, the irradiated body hits a temperature where income=outgoing. More greenhouse gases just change the radiation/heat profile of the planet so that the point where income=outgoing ends up at a higher temperature.
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.
> 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.)
One way to understand this cooling effect is that it occurs because at wavelengths where greenhouse gases are not substantially absorptive, heat can effectively escape out (or at least get absorbed and sent back to you at a higher altitude). The actual mechanisms are more complex than I'm describing as the atmosphere's temperature and composition varies with altitude, but the net effect from the perspective of a surface facing the sky is that, if you're at the same temperature as the air around you, you will radiate more heat out than the sky sends back to you.
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.
Huh. So this is why cars parked on one side of a street (with no tree cover) will be covered in condensation, while those parked on the other side (which has tree cover) will not?
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.