Believe it or not, this is already happening by many more miles than one foot. The earth has an elliptical orbit around the sun. At the closest point in our year, usually around January 4th, we are at the perihelion and at aphelion around July 3rd we are at our farthest point. It is not so much our closeness to the sun that determines what happens to us on terra as the angle of the sun. Thus in the northern hemisphere when the sun is closest is our winter and when the sun is farthest away it is our summer.
Therefore, nothing different would happen on Earth if we moved a foot closer to the sun because we are already doing that (and much more) every single year!