pyro-
before vowels pyr-, word-forming element form meaning "fire," from Greek pyr (genitive pyros) "fire, funeral fire,

before vowels anem-, word-forming element meaning "wind," from Greek anemos "wind," from PIE root *ane- "to breathe."
They aren't following a strict formula though. We have "Hydatos" instead of Hydros; Pagos instead of Cryos, etc. They're named in Sharlyan fashion and from Sage abilities, we know now that Sharlyan uses ancient greek/proto-indo European.