Não, Jon não é imune ao fogo. Lembre-se da primeira temporada, quando um feiticeiro ataca Castle Black e tenta matar Lorde Comandante Mormont. Jon joga uma lanterna nele e queima a mão no processo.

Jon tried to shout, but his voice was gone. Staggering to his feet, he kicked the arm away and snatched the lamp from the Old Bear's fingers. The flame flickered and almost died. "Burn!" the raven cawed. "Burn, burn, burn!"

Spinning, Jon saw the drapes he'd ripped from the window. He flung the lamp into the puddled cloth with both hands. Metal crunched, glass shattered, oil spewed, and the hangings went up in a great whoosh of flame. The heat of it on his face was sweeter than any kiss Jon had ever known. "Ghost!" he shouted.

The direwolf wrenched free and came to him as the wight struggled to rise, dark snakes spilling from the great wound in its belly. Jon plunged his hand into the flames, grabbed a fistful of the burning drapes, and whipped them at the dead man. Let it burn, he prayed as the cloth smothered the corpse, gods, please, please, let it burn.
_{A Game of Thrones, Jon VII}

Além disso, os Targaryens nunca foram feitos para serem imunes ao fogo sempre:

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.
_{So Spake Martin - Egg and the Targaryens}

Targaryens não são à prova de fogo.

De uma entrevista com GRRM.

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.

Se Daenarys é realmente à prova de fogo, há algumas leituras muito interessantes sobre Reddit. Parte disso explica que no universo ela não é à prova de fogo.

Dany hit him. “No,” she screamed, swinging the lash with all the strength that she had in her. The dragon jerked his head back. “No,” she screamed again. “NO!” The barbs raked along his snout. Drogon rose, his wings covering her in shadow. Dany swung the lash at his scaled belly, back and forth until her arm began to ache. His long serpentine neck bent like an archer’s bow. With a hisssssss, he spat black fire down at her. Dany darted underneath the flames, swinging the whip and shouting, “No, no, no. Get DOWN!” His answering roar was full of fear and fury, full of pain. His wings beat once, twice [...]
Her skin was pink and tender, and a pale milky fluid was leaking from her cracked palms, but her burns were healing.

---

_{A Dance With Dragons, Page 699 Google Books}

Como mostra seu diálogo interno, e as queimaduras posteriores daenárias claramente não são completamente à prova de fogo.

Tem certeza de que ele foi realmente atingido pelo fogo?

Ignorando todas as perguntas das regras da TV versus do livro sobre se Targaryens é consistentemente imune ao fogo, vimos na temporada 1, quando Daenerys entrou no fogo e sobreviveu, suas roupas não. Mesmo se ela é imune ao calor por causa de seu sangue Targaryen, o tecido não é.

Mesmo que Jon seja, em teoria, imune ao fogo como Dany, se ele tivesse sido atingido diretamente pelo fogo do dragão, teríamos visto algum dano de fogo em sua armadura e roupas, mas não o fizemos.