We've seen how the Sun will appear, in Luminosity and Temperature, as traced in its motion on the HR Diagram as it ages and leaves the Main Sequence. As the Hydrogen is used up, the central core begins to collapse, increasing the central temperature. This increases the Hydrogen fusion, making the core extremely hot, and pushes off the outer layers of the Sun.

At some point, the Sun's core collapses far enough to obtain central temperatures high enough to fuse Helium

3 ⁴He ---> ¹²C

into Carbon in the central core. Early on, Hydrogen fusion is still occurring in an outer shell of the central core. From the outside, the Sun will have grown first physically larger AND then also cooler.

As the core runs out of He, it continues to collapse and heat up. The sun develops ``flakes'' of carbon and silicate, condensed out of the cool, expanding Solar atmosphere. Now, the radiation from the central core can even more effectively push the atmosphere out and away. At this point, the sun will have grown to such a radius, it would engulf Mercury and Venus!