Hello from the NWT - stove question

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Let's say it's -40 with a breeze. How much cooling will occur towards the top of a chimney? Or, more regularly here, -20...

It must be quite significant. Does anyone have a rough guideline?

My chimney is 7' above roofline. I don't like that, but it had to be to fit with the inside rooms.
The only way to tell that is with a probe placed way up there! It may not be as much as we imagine. The stove is going to be drafting something fierce and you’re probably going to be raising stack temps naturally. Throw in 2 stories of it being internal and you may be able to keep them up! Of course, I may be completely wrong! I’ve never run past the -mid 20sF. I guess that isn’t too far away. Conversion says that was -31C.
-30C is where real cold starts to start.

I would have already been monitoring the top if I didn't have a steep steel roof which requires a bit of a "production" to get up there. Curious is all re temps at the top.