No, Jon is not immune to fire. Remember in the first season, when a wight attacks Castle Black and tries to kill Lord Commander Mormont. Jon throws a lantern at it, and burns his hand in the process.
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
Additionally, Targaryens were never meant to be immune to fire allways:
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
