The sun will move to the cooler and brighter part of the diagram.
Explanation:
When the sun becomes a red giant, it means it is fusing hydrogen in its outer shells and the inner core has exhausted its hydrogen fuel. Because the sun has a smaller mass relative to other big stars, its does not have enough gravity to fuse helium. Therefore, the radiant and thermal pressure from the contraction of the core overpowers the gravitational pull causing the outer shells to grow and move away from the core. The general temperatures of the sun slightly decreases (hence is cooler) but luminosity (brightness) increases because of the increase in star size. The star grows to over 250 time is current size 'swallowing' the earth too.
