Jatayu and Sampati
An old Indian epic poem called Ramayana contains a similar tale of what happens when you fly too close the sun. Jatayu and Sampati are two demigods in the shape of birds, who also happen to be brothers. One day, Jatayu and Sampati decide to try to fly to the home of the sun god, Suryalock. (Notice that this myth includes a visit to the sun, just like Phaeton's story.) They fly higher and higher, until all of a sudden they are really hot, because duh, they were next to the sun.
Realizing the danger of their situation, Sampati shields his younger brother Jatayu from the sun's heat. As a result, both of Sampati's wings are burned off, and he careens down to the ground. (Sound familiar? Ahem, Icarus. Ahem, Phaeton.) Although Jatayu's wings are only partially burnt, he also falls. Eventually, lucky Jatayu is able to recover and have a few more adventures, like trying to save the princess Sita from the lecherous King Ravana. Sampati, unfortunately, never recovers from this incident, and lives a sad, flightless life in the forest. Just like in the myth of Phaeton and Icarus, the tale of Jatayu and Sampati warns readers not to be reckless or overstep their bounds.