In order to hatch a dragon in A Song of Ice and Fire, the eggs must be
heated to an incredible heat
Who said that? Dragon incubators do not exist in Planetos.
Hatching a dragon is not that simple.
All the accomplishments of the Dragon Lords were thanks to Blood magic. They possibly used blood magic to hatch dragons from Wyverns and certainly used blood magic to bind Dragons to themselves.
In Septon Barth's Dragons, Wyrms, and Wyverns, he speculated that
the bloodmages of Valyria used wyvern stock to create dragons.
Though the bloodmages were alleged to have experimented mightily with
their unnatural arts, this claim is considered far-fetched by most
maesters, among them Maester Vanyon's Against the Unnatural contains
certain proofs of dragons having existed in Westeros even in the
earliest of days, before Valyria rose to be a power.
- Beyond the Free Cities: Sothoryos
"What feeds a dragon's fire?" Marwyn seated himself upon a stool.
"All Valyrian sorcery was rooted in blood or fire. The sorcerers
of the Freehold could see across mountains, seas, and deserts with one
of these glass candles. They could enter a man's dreams and give him
visions, and speak to one another half a world apart, seated before
their candles. Do you think that might be useful,
AFFC - Samwell V
How did Daenerys do it?
The kind of Blood magic shown there is simple, you provide sacrifice of something and you get something in return.
"You'll have gold, horses, whatever you like."
"It is not a matter of gold or horses. This is bloodmagic, lady.
Only death may pay for life."
AGOT - Daenerys VIII
The eggs that Daenerys had were very old. They had turned into stones by the time they came into her possession. Fate of other dragon eggs would be similar since last living dragon died in reign of King Aegon III centuries ago.
Even Illyrio, who gave her the eggs, had no idea that they would hatch.
"I know that he gave me my dragon eggs."
He snorted. "If he'd known they were like to hatch, he'd would have
sat on them himself."
That made her smile despite herself. "Oh, I have no doubt of that,
ser. I know Illyrio better than you think. I was a child when I left
his manse in Pentos to wed my sun-and-stars, but I was neither deaf
nor blind. And I am no child now."
ACOK - Daenerys
Daenerys however figured out a way. She figured out the nature of Mirri Maz Duur's magic and cleverly improvised.
She provided sacrifice of:
- Khal Drogo
- A horse.1
- Mirri Maz Duur herself
"You will not hear me scream," Mirri responded as the oil dripped from
her hair and soaked her clothing.
"I will," Dany said, "but it is not your screams I want, only your
life. I remember what you told me. Only death can pay for life."
Mirri Maz Duur opened her mouth, but made no reply. As she stepped
away, Dany saw that the contempt was gone from the maegi's flat black
eyes; in its place was something that might have been fear. Then there
was nothing to be done but watch the sun and look for the first
AGOT - Daenerys X
For coup de grâce, she climbed into the pyre herself. As a result, the stone eggs came back to life and dragons were hatched.
This was a one-time magical event. Only time it ever succeeded. GRRM cleared it up.
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
Not to mention, Daenerys might actually be someone very special. As Maester Aemon believed:
What fools we were, who thought ourselves so wise! The error crept in
from the translation. Dragons are neither male nor female, Barth saw
the truth of that, but now one and now the other, as changeable as
flame. The language misled us all for a thousand years. Daenerys is
the one, born amidst salt and smoke. The dragons prove it.
AFFC - Samwell IV
That does not mean there were no attempts to rehatch dragons from stone-eggs before. King Aegon III asked mages and other scholars from Essos to hatch dragons from his cache of eggs. It failed. Prince Aerion drank wildfire thinking that it would transform him into a dragon. It failed. King Aegon V tried to use wildfire to hatch dragons, it failed and House Targaryen was wiped out save one lonely branch of Jaehaerys II Targaryen.
The look Stannis gave her was dark. "Nine mages crossed the sea to
hatch Aegon the Third's cache of eggs. Baelor the Blessed prayed over
his for half a year. Aegon the Fourth built dragons of wood and iron.
Aerion Brightflame drank wildfire to transform himself. The mages
failed, King Baelor's prayers went unanswered, the wooden dragons
burned, and Prince Aerion died screaming."
ASOS - Davos
There were dragons here two hundred years ago, Sam found himself
thinking, as he watched the cage making a slow descent. They would
just have flown to the top of the Wall. Queen Alysanne had visited
Castle Black on her dragon, and Jaehaerys, her king, had come after
her on his own. Could Silverwing have left an egg behind? Or had
Stannis found one egg on Dragonstone? Even if he has an egg, how can
he hope to quicken it? Baelor the Blessed had prayed over his eggs,
and other Targaryens had sought to hatch theirs with sorcery. All they
got for it was farce and tragedy.
AFFC - Samwell I
What became of the dream of dragons was a grievous tragedy born in a
moment of joy. In the fateful year 259 AC, the king summoned many of
those closest to him to Summerhall, his favorite castle, there to
celebrate the impending birth of his first great-grandchild, a boy
later named Rhaegar, to his grandson Aerys and granddaughter Rhaella,
the children of Prince Jaehaerys.
It is unfortunate that the tragedy that transpired at Summerhall left
very few witnesses alive, and those who survived would not speak of
it. A tantalizing page of Gyldayn's history—surely one of the very
last written before his own death—hints at much, but the ink that was
spilled over it in some mishap blotted out too much.
...the blood of the dragon gathered in one... ...seven eggs, to honor the seven gods, though the king's own septon had warned...
...pyromancers... ...wild fire... ...flames grew out of
control...towering...burned so hot that... ...died, but for the valor
of the Lord Comman...
TWOIAF - The Targaryen Kings: Aegon
There is no indication whether other people in possession of Dragon eggs ever attempted to hatch them. They would have thought it futile given that eggs were dead stones. They were used as valuable commodity, not as livestock. So in conclusion:
- Blood magic is required to hatch dragons.
- Existing eggs in current timeline are essentially stones.
- Daenerys' feat was a one-time magical event, a miracle.
Also see: How many dragons have ever existed in Westeros and what became of them?
1. It is possible that it may have been Rhaego's soul in Drogo (So Drogo would count as two) or Daenerys herself (Although she never died). Third sacrifice is unconfirmed as of now.