Earth is not getting closer to the Sun: if it did, the year would become much shorter, and astronomers would notice the change long before our eyes (or Earth climate) will respond to it.

By pure chance, the visual sizes of Moon and Sun in the sky are almost the same. Actually, both vary, since the orbits of both Earth and Moon are slightly elliptic. Usually the Moon appears slightly bigger, so when it passes between us and the Sun we can get (in select areas) total eclipses of the Sun, lasting a few minutes. But sometimes it is smaller, and then we only get annular (=ring shaped) eclipses of the Sun, in which the Moon, even when crossing our line of view right in front of the center of the Sun, only leaves a bright ring all around it. If Earth were getting closer to the Sun, such eclipses should become the prevalent kind, but they don't do so.

The heat received from sunlight must equal the heat radiated back to space--otherwise the Earth might warm up to where oceans boil away. As explained elsewhere, greenhouse gases impede the flow of heat from the ground to the high atmosphere (from where it is radiated to space), and as a result, climate gets a bit warmer. But in addition, the area on the Earth involved in returning heat to space expands poleward, and that's why icecaps tend to melt.