One who's personality traits personify the personality traits of the common Dragon.
Like Lionhearted (a courageous type of person) this means that they are arrogant (but justifiably so) and angry types due to their reptilian nature (see Reptilian Brain).
Not to be confused with Dragonkin. Being Dragonhearted is to do with personality traits, not spiritual beliefs.
Other examples of anthropomorphizing the Heart include: Lionhearted (Courageous), Owlhearted (Intellectual) and Serpenthearted (Selfish).