There is a simple fix for overheating--just reduce the amount of sunlight hitting the earth. You do this with artificial "clouds", which can be placed in stationery orbit between the earth and the sun, to reduce the amount of sunlight by about 1% or 2%. The "clouds" would be invisible since you would have to look direclty into the sun to see them (and even then they would be pinpricks in size.)
Next problem?
This is an interesting concept.
I read about another proposal (waaaaay in the future) to install a geostationary lens over Mars in front of the Sun to warm it to Earth-like temps.
Didn't Montgomery Burns already try that?