Phaeton's Dad, Helios, is the Titan god of the sun. In some versions of the story, Helios is actually Phaeton's Granddaddy, but whatevs... we think the story is better when he's Phaeton's Dad. The story of Phaeton shows a chiller side of Helios that you don't get to see in lot of other tales. Yeah, he's the great and powerful god of the sun, but he's also a caring, concerned father. When Phaeton shows up and asks if Helios is his Dad, Helios could be like, "Get lost, pipsqueak. If I wanted to talk to you, I'd actually come by on Christmas. Help yourself to a Junior Mint on the way out." Instead, Helios tries to show Phaeton that he cares by offering his son anything he wants in the world. Sincere, though not the most responsible act of parenting.
In the end, though, Helios's generous gesture ends up causing his son's death (whoopsies). Phaeton demands that the god allow him to drive the sun chariot across the sky. Helios knows this is a crummy plan, and he begs Phaeton to reconsider. Once again, he shows that he really cares about Phaeton by laying out all the dangers involved: unruly flaming horses, killer sky monsters, etc. Unfortunately, Phaeton doesn't listen to his dear old dad and goes down in flames. Ironically, it's Helios's care for his son that causes the boy's doom, the oldest facepalm on the books.