Is there a Greek myth of some sort of a god, human, or other creature living in the sun?
So far as I know the Greco-Roman myths about the sun consistently refer to it as an object, usually the wheel of a chariot which is handled by Apollo or Helios. The Greeks didn't personify or anthropomorphize the sun.
The Hindu Mother goddess lives within the Sun thereby liberating the Sun's energy to the universe. Since then, this form of the Goddess has been known as Kushmanda, namely for her power and capability to live inside the Sun. The glow and radiance of her body are as luminous as that of the Sun.