The Targaryens are not immune to fire, heat or molten metal. According to George R.R. Martin (the author of the books, if anyone was in doubt) the birth of the dragons was a special magical event.
Here are a few sources:
Is Daenerys Targaryen immune to fire? - Scifi.StackExchange
(Snippet from an interview)
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.
A Wiki of Ice and Fire
The Targaryens can tolerate a bit more heat than most ordinary people, though they are by no means immune to fire.
But then again. These statements are most likely about the books and not the TV series. So it is possible that it is changed in the series.
This wiki, which seems to be mostly about the series, states the following:
Targaryens have some common genetic traits such as silver-white hair. Some members of the family are also immune to the effects of fire, extreme heat, or high temperatures.
Remember though that these wikis are maintained by fans that might have the same misconception about the immunity.