On Venus? Still won't get you close to habitability. I'm not sure how long it'd take it to radiate its excess heat away, but it'd be a long time. And then you've still got an atmosphere which is horrendously poisonous and corrosive.
Besides, once you've got the technology and materials to build a solar shield which is an appreciable fraction of planet-sized, you might be questioning whether a planet is really the best place to live. Why not just live in your giant space stations?
Venus is 0.722 AU from the sun so it revives about twice the energy per m^2 than the earth does. Even if you where to remove the greenhouse gas problem it would be nowhere close to habitable.
If you look at the Day/Night cycle on earth 1 week without sunlight would probably drop Venus into sub zero temperatures. Depending on how much over kill you provided a few months would be plenty of time to cool down to reasonable levels.
Even if you where to remove the greenhouse gas problem it would be nowhere close to habitable.
Per unit surface area, how much less sunlight do you get at Earth's poles than at Earth's equator? That's too hard for me to figure out off the top of my head (taking the seasons into account), but I'm pretty sure it's at least a factor of two. So I think a planet with an Earthlike atmosphere in a Venusian orbit would be habitable in the polar regions.
The summer temperature at earth's north pole is for June, July and August is 0°C or 273K. Assuming pure radiative cooling, twice the incoming sunlight (2 * 273K^4)^1/4 = 50.85 degrees Celsius or 123.53 degrees Fahrenheit for three months at a time. Which is at the outer edge of habitable.
However, the atmospheric pressure at the planet's surface is 92 times that of the Earth. So the difference in temperature in the summer is far less than the earth because a lot more energy is transferred to the poles. If you where to somehow remove that atmosphere not just change it's composition the poles may just barely become habitable.
Also wind speed is temperature dependent (Wind being a heat engine) so even with earths atmosphere a lot more energy would make it to the poles in summer.
Why you need to build planet-sized shield? Why not pollute top layers of atmosphere with something bright? SO2 will be good choice. One satellite with few tons of SO2 can pollute Venus atmosphere in few weeks, and it will stay polluted for thousands of years.
There is already a crap-ton of SO2 in Venus's atmosphere (about 40 teratonnes, to be precise), that's where the sulfuric acid clouds come from. If we sent a supertanker full of SO2 to Venus every single day for a thousand years we wouldn't affect the amount of SO2 in the atmosphere by even 1%.
Besides, once you've got the technology and materials to build a solar shield which is an appreciable fraction of planet-sized, you might be questioning whether a planet is really the best place to live. Why not just live in your giant space stations?