My theory on the third head of the dragon of the Song of Ice and Fire is that it could possibly have been Joffrey Baratheon. Cersei was infatuated with Rhaegar, she even said he was the most beautiful man in the world. Did anything ever happen with that? There is usually a crazy bad seed in the line. Aerys, the mad king, etc. and now Joffrey. It makes sense to me, what do you think?
I think Jon is the second head, as being the son of Lyanna and Rhaegar that Ned disguised as being a bastard. She died of unknown reasons, which was probably child birth, her last words were, "Promise me, Ned." I believe this could mean that Ned needs to conceal his true identity to keep him safe. Jon Snow is the "Prince that was promised." A Song of Ice and Fire. BOOM!