Gera, you don't need to regulate the Sun. I'm not a climate scientist, but, simplistically, the whole thing is based on energy conservation:
{Amount of energy received from Sun's radiation} + {Energy generated on Earth} = {Change in Earth's internal energy} + {Energy re-radiated into space}.
{Amount of energy received from Sun's radiation} and {Energy re-radiated into space} is received from satellites and/or computed. {Energy generate on Earth} is small compared to other terms.
We are after the {Change in Earth's internal energy}, which depends on how much energy is trapped in Earth's atmosphere. This, in turn, depends on chemical composition of said atmosphere. For instance, water vapor "traps" solar energy and makes it nice and comfortable for us to live here.
If more energy is trapped, temperature will rise and makes it not so comfortable.
Why do you need to regulate the Sun?