WARNING: The following contains spoilers for One Piece Chapter #1023, "Spitting Image," by Eiichiro Oda, Stephen Paul and Vanessa Satone, available in English via Manga Plus and Viz Media.
As a former member of Judge Vinsmoke's MADS group, Queen is familiar with how the scientist thinks in One Piece. He knows the Vinsmoke children are cyborgs and until Sanji clarified his own physiology in Chapter #1023 of the manga, Queen thought the chef was just another result of Judge's experimentation. In the chapter, Queen counters that a normal human can't light their leg on fire as Sanji can, then drops an interesting name, questioning Sanji's true identity, that King seems to react to -- Lunarians.
This appears to be the name of the fire-controlling race King has been said to be a member of. They lived above the Red Line before Mary Geoise was constructed, and were considered gods if Whitebeard's drunk storytelling is to be believed. Though they are now believed to be extinct, we know King can control flames on a larger scale, so could Sanji be a descendant of this race of people? We know the fire isn't caused by any type of Haki, and he says he's 100-percent human. Could the fire be a result of genetics? Let's look into it.
Given Sanji's father's enormous size, perhaps the Vinsmokes of One Piece are descended from Lunarians. While it's highly doubtful Sanji is a full-blooded Lunarian himself, it's possible that somewhere in the distant past, a Lunarian mated with a human which resulted in Judge's family. The fire powers would have been a recessive trait, and since the other children weren't allowed to express extreme emotions like Sanji, they never awakened their abilities. Sanji only learned about it when he felt extreme anger while training on Momoiro Isle. We don't know whether the wings on King's back are a Lunarian trait, but it seems likely his large stature is if this theory holds true.
During the fight with King and Queen, the latter says, "Does a human burn like that?! I know you ain't Lunarian!!" Sanji replies with "I do!! The heat of my passion surpasses the temperature of flame!!!" The "I do" portion of his speech is most likely referring to the "human burning" part of Queen's question, but it could be Oda's way of hinting that Sanji is part Lunarian, even if Sanji himself doesn't know it yet.
It's also possible the Lunarians have nothing to do with Sanji's powers and that it's a side effect of his father's experimentation. While Sora took medicine during her pregnancy to keep her children human, Sanji was the only one it worked on. Perhaps some part of the experiment took hold but is only triggered by Sanji's extreme emotions. He was deemed a failure because of his emotions, but they could be the very source of his abilities.
In the end, Sanji's powers may come from the unique combination of his father's experiments and his mother's love. For now, One Piece fans are left to speculate as the story continues to unfold.
