In A Song of Ice and Fire men of the Night's Watch kill

Jon Snow.

Why didn't they burn his body? Didn't they fear that he may become a wight?

The below speculates with the known information on what could possibly be the reasons though we don't know for sure. However, it is worth noting initially that the dead cannot be turned into wights south of the Wall. White Walkers have to use their magic to turn the dead and the Wall has magic that can stop the "dead passing" which probably means it stops their magic also.

Now I'm not sure if the Brothers know this or not but it is worth noting that it isn't strictly necessary to burn their bodies. Although Jon does state that those in the tunnel who died against the giant were to be burned so potentially they think either all need to be burned of being in the tunnel is a bit of a grey area so were just being safe.

A Song of Ice and Fire

We don’t know because we see nothing of Jon after the stabbing and murder.

Jon fell to his knees. He found the dagger's hilt and wrenched it free. In the cold night air the wound was smoking. "Ghost," he whispered. Pain washed over him. Stick them with the pointy end. When the third dagger took him between the shoulder blades, he gave a grunt and fell face-first into the snow. He never felt the fourth knife. Only the cold...

_{A Dance with Dragons, Jon XIII}

That is the last paragraph of the last chapter we have of a perspective at the Wall so we don't know anything that happens afterwards just yet.

Game of Thrones

The last we see of Jon in Season 5 is him dying in a puddle of his own blood.

The brothers retreat, leaving Jon to die alone on the ground, bleeding out. The light goes out of his open eyes as we fade on Season 5.

_{Game of Thrones, Season 5 Episode 10, "Mother’s Mercy" - Official Script}

Season 6 then opens with Davos spotting Jon’s body in the snow.

EXT. CASTLE BLACK - NIGHT

Pan down from the inside of The Wall towards Castle Black. GHOST is howling. Slow zoom to JON SNOW's body, lying in the snow. A sign with the word "TRAITOR" is posted on a beam behind him. Closeup on JON SNOW. He is staring upwards, lifelessly. GHOST howls louder and pushes against the door to his pen.

CUT TO: CASTLE BLACK - DAVOS' CHAMBER

DAVOS hears GHOST's howling and exits, then peers across the courtyard and sees JON SNOW's body. He immediately runs down the steps. He slows as he approaches JON SNOW's body. Other brothers of the Night's Watch approach. DAVOS kneels beside JON SNOW's body.

NIGHT'S WATCHMAN: It's the Lord Commander!

DOLOROUS EDD and other Night's Watchmen rush up behind DAVOS.

DAVOS: Help me get him inside.

The other Night's Watch brothers pick up JON SNOW's body and carry it away. DAVOS remains, staring at the left over pool of blood.

_{Game of Thrones, Season 6 Episode 1, "The Red Woman"}

Whilst we don’t know for sure why Thorne and the others left Jon's body there we can speculate on the following.

• To send a message to the others that anyone else that goes against what they want will be killed too.




• To hide that it was them, whilst it obviously was them, not being caught at the scene could help their case if they needed to defend themselves later on.

Although of course considering he openly admits it later on so he can bend the other Brothers to his way of thinking it is almost certainly done to send a message. He needs the other brothers to understand what happened and why it happened so they can come into his line of thinking.

ALLISER THORNE: We’ve committed treason, all of us. Jon Snow was my Lord Commander. I had no love for him. That was no secret. But I never once disobeyed an order. Loyalty is the foundation on which the Night’s Watch is built, and the Watch means everything to me. I have given my life, we have all given our lives to the Night’s Watch. Jon Snow was going to destroy the Night’s Watch. He let the wildlings through our gates, as no Lord Commander has ever done before. He gave them the very land on which they reaved and raped and murdered. Lord Commander Snow did what he thought was right, I’ve no doubt about that. And what he thought was right would have been the end of us. He thrust a terrible choice upon us, and we made it.

The men begin to murmur among themselves.

_{Game of Thrones, Season 6 Episode 1, "The Red Woman"}

Or they may have been going to actually get some firewood to burn him, we simply don't have enough information on the time frame from them killing him to Davos finding him. Of course considering the above this seems unlikely.

Your post is tagged both with the books and show tags so I'll cover both.

In the books, the last we see of Jon is the stabbing, so for all we know they do burn the body after. It's simply unknown what happens next still.

In the show, they give no reason for not burning it immediately, but it's not long after that the Onion Knight and Edd and the rest abscond with the corpse to get Mel to bring him back, so presumably the option wasn't on the table for long.