Official Word of God says:

> Lastly, some fans are reading too much into the scene in GAME OF THRONES where the dragons are born -- which is to say, it was never the case that all Targaryens are immune to all fire at all times.

Source: http://www.westeros.org/Citadel/SSM/Entry/945/

Also this (sourced from http://www.dakkadakka.com/dakkaforum/posts/list/449541.page?userfilterid=33891):

> Granny: Do Targaryens become immune to fire once they "bond" to their dragons?

> George_RR_Martin: Granny, thanks for asking that. It gives me a chance to clear up a common misconception. TARGARYENS ARE NOT IMMUNE TO FIRE! The birth of Dany's dragons was unique, magical, wonderous, a miracle. She is called The Unburnt because she walked into the flames and lived. But her brother sure as hell wasn't immune to that molten gold.

> Revanshe: So she won't be able to do it again?

> George_RR_Martin: Probably not.