Question

Are red giants cooler than when they were main sequence stars?

Answer 1

Yes and No; Depends on Mass

Explanation:

If you were referring to the stellar core:

If the star has a solar mass of more than `M_"☉"` 8, then while in red giant phase, it will start to fuse carbon and oxygen in its core, and the minimum temperature needed for this is 500 million K, around 487 Million K more than the core temperature of Main Sequence Stars. If the mass of the star is not more than `M_"☉"` 8, then the red giant will only fuse helium, and the core will be roughly 100 million K. This is still hotter than most main sequence stars that burn Hydrogen in their cores at 13 Million K and above.

If you were referring to the surface temperature:

Most main sequence stars best red giants in surface temperatures simply because the red giants are so much larger, and the heat from the core is spread out over a larger area.