It’s…ambiguous. He sheathed it in one fluid motion, as in it looked like that was what he was already doing… but he could have just taken it out and then reversed the motion when Criston shows up. There seems to be very little reason for his sword to have been out for any other purpose, the enemy was well away and contained within the castle, he was in no danger. And he obviously did not have the sword out while he was riding Vaghar.
The scene begins with Aemond approaching the wreck lifting his unsheathed sword, as if to strike a blow. So I think he was just about to do it, but when Cole calls out to him, he turns and sheaths his sword instead.
Which should be another clue to Cole about what was going to happen: If Aemond claims he was simply going to put the Sunfyre out of his misery, then why didn’t he proceed with that mercy after Cole’s arrival? The resheathing of the sword reflects Aemond’s true intentions. I doubt Cole will figure it out, though.
Or care if he did figure it out, he seems to favor Aemond more.
He does favor Aemond, but he seems loyal to Aegon, too. He is genuinely distressed over the accident. He rallied the troops before the battle commenced when he realized Aegon had just flown in to join them.
Aegon made him the Hand. If he figures out that Aemond is attempting to assassinate Aegon, will he make the mental leap to understand that Hands are probably more expendable than brothers?
Long interesting post by George RR Martin on the nature of dragons. Didn’t know where else to post it, there are no spoilers for the story other than what has already been on TV.
Interesting read. Thanks for posting it!
He could claim the opposite. That he was worried Sunfyre might still have some life in him. Not enough to survive, but enough to lash out at the first thing to approach it, like a blind fighter trapped in a corner. The sword was to protect him from Sunfyre as he bravely approached to render aid to his brother, the King, the story might go.
To quote an oft-used utterance of Aemond’s, hmmmmm.
But then why did he abandon the effort just because Cole walked up? Was his brother in any less need of aid with Cole on the scene?
Who says he abandoned the effort? It was just coincidentally at that moment that he concluded Sunfyre was DOA. He sheathed the sword to be able to better assist his brother, the King, and was relieved to find Cole approaching to assist.
But Sunfyre was still making noises of agony throughout that scene, even as and after Cole walked up.
Kind of a hard sell to claim Aemond still intended to aid his brother when he just walks off after Cole’s arrival. 
Unless Aegon was dead, or Aemond believed him to be. But I think he’s still alive.
(We’re just being silly, really, since we’ll find out on Sunday!)
HBO is doing something funky with the episode titles with this season. During week 2 they didn’t even have an episode title on release - the HBO app itself, IMDB, and other sources just listed it as “episode 2” until the day after release. This episode, on IMDB called it “a Dance of Dragons” but it’s now listed as “The Red Dragon and the Gold”. I wasn’t the only one to be thrown by that, for example this reddit thread called it “A Dance of Dragons” but later edited the episode name within the description but not the original title it was posted under.
I’ll ask a mod to edit the title but wtf is HBO doing?
I watched it Monday night and the correct title was on HBO. But next one still isn’t out from what I can see, they keep it close to the chest.
That could almost be its own title…
I noticed the title had been changed and thought they didn’t want to spoil which dragons would be “dancing”.
My bad, guys. I’m late with the episode 5 thread.
I think it’s IMDb that is the problem. I watched this episode that Sunday night on MAX a few minutes after it started airing on HBO and it was listed there with the correct title “The Red Dragon and the Gold”