Why does dragon fire from Game of Thrones leave bones?

Before the dragons from the TV series have grown we learned from the pyromancer that wildfire was the closest they could get to dragon fire. According to him the wildfire could burn through metal, stone, and flesh.

We could also saw how dragon fire could destroy the keep leaving great big holes in the walls.

Later when Dany's dragons grew up and started hunting we could see that they ate goats and a poor child leaving nothing but burned bones behind. How come the bones were left if the fire is so strong?

Also, if the fire was that strong, how does Dany expect that a metal chain and a door could keep them?

Answer

How come the bones were left if the fire is so strong?

You must bear in mind that we had no idea how exactly the bones came to be. Drogon was said to have been responsible for them, but there are a few scenarios which this could have happened:

• he might have just been burning something nearby, or


• might have just devoured the carcass, passing the bones (which were scorched due to the insides of the dragon being extremely hot, or


• the bones might have been cooked in an oven as suspected by Dany (for the sheep anyway)

Also, if the fire was that strong, how does Dany expect that a metal chain and a door could keep them?

Chains Were Made to be Broken

The metal chains were only truly to get the dragons into the pit, beyond that there was no guarantee that the chains would hold. In fact, Viserion had actually broken through his:

^{[A Dance With Dragons spoiler]}

The dragons craned their necks around, gazing at them with burning eyes. Viserion had shattered one chain and melted the others. He clung to the roof of the pit like some huge white bat, his claws dug deep into the burnt and crumbling bricks. Rhaegal, still chained, was gnawing on the carcass of a bull. The bones on the floor of the pit were deeper than the last time she had been down here, and the walls and floors were black and grey, more ash than brick. They would not hold much longer … but behind them was only earth and stone. Can dragons tunnel through rock, like the firewyrms of old Valyria? She hoped not.
^{-A Song of Ice and Fire: A Dance With Dragons, Part Two - Blood and Fire (Daenerys).}

Perhaps given time, they could burn through the walls/doors (but that's just conjecture).
Take note also that there are a pile of bones. We don't know if they are scorched or not, but that definitely shows that an encounter with a dragon can leave bones behind!

The Blood of Old Valyria
There are some whom the dragons might take a liking to, or at least tolerate:

^{[A Dance With Dragons spoiler]}

Brown Ben Plumm is one such person; he can trace his ancestry back to Old Valyria, and there are many mentions of how the dragons took a liking to him, especially this one:

[Tyrion:] Your branch sprouted from a stone spit across the narrow sea, no doubt. A younger son of Viserys Plumm, I’d wager. The queen’s dragons were fond of you, were they not?”
That seemed to amuse the sellsword. [Plumm:]“Who told you that?”
[Tyrion:]“No one. Most of the stories you hear about dragons are fodder for fools. Talking dragons, dragons hoarding gold and gems, dragons with four legs and bellies big as elephants, dragons riddling with sphinxes … nonsense, all of it. But there are truths in the old books as well. Not only do I know that the queen’s dragons took to you, but I know why.”
[Plumm:]“My mother said my father had a drop of dragon blood.”
^{-A Song of Ice and Fire: A Dance With Dragons, Part Two - Blood and Fire (Tyrion).}

Using this to one's advantage can help to provide a means for controlling dragons.