We all remember Daenerys's quote right after Viserys's death (Season 1 episode 6: "A Golden Crown", and A Game of Thrones chapter Daenerys V):
He was no dragon. Fire cannot kill a dragon.
However, are we sure that this is true? Can a dragon be killed/harmed by fire?
We know that a lot of dragons died during the Doom of Valyria, the cataclysm of an unspecified nature which did contain a lot of fire. In The World of Ice & Fire, there is a picture of dragon with fire on his back with the description A dragon burning during the Doom.. It doesn't say this dragon died because of the fire, but it does prove that dragons can burn (unless we attribute this to the unreliable narrator).
On the other hand, dragons breathe fire and they seem unharmed by their own fiery breath. Also, Daenerys hatched her dragons in pyre and that did not harm her newly-hatched dragons.
So was the fire during the Doom of Valyria simply much hotter than regular fire, and is that the reason it could hurt dragons? Or did the fire during the Doom of Valyria not hurt the dragons, but did they die of other causes (e.g. debris flying around)?
As a side, could a dragon harm/kill another dragon with its fiery breath? Is there any example of this, for instance during the Dance of the Dragons?