Wood Stove installation w/vaulted ceiling

I think I have a bit of a dilemma, because on one hand if I don't have a long enough pipe it might not draw well.

On the other hand, half of that 14' feet of pipe will be outside, so it would be more likely that the pipe would cool down so much that it would prevent the exhaust from rising properly.

I'm hoping the 9' 6" of pipe will be enough, there are no turns in it, so maybe it will be fine. I hope so, due to the fact that any extra pipe exposed to the cold could create another problem, especially in colder weather. Not only that, but an extra 4' 6" would look odd, as the pitch of the roof isn't very steep, so the pipe would be quite high above the ridge of the roof.

Yes, as I stated in my post above, the extra pipe exposed to the outside is a concern for me, as it could cool the gases in the pipe to the point that they won't rise properly, which would create a draft problem, and likely cause the chimney to become clogged.

The more pipe outside, the more likely the problem will occur, so for now I'm going with the shorter pipe, and crossed fingers.

I'm just wondering about that wall thimble, I don't want my pipe coming out of the roof at an odd angle.

I've installed a few stoves, but they were all piped through a wall into an existing flue, never straight up through the roof.

Yeah, I'll be using stainless chimney pipe from through the thimble all the way to the cap.

I'm thinking that as the chimney cools the gases in it cool as well, and as a result they slow down, causing a lack of draw.

Hot air rises, but as that hot air cools it slows down.

I've heard people complain that their stove puffs smoke some times, but only during really cold weather, so it makes sense.