The air at the top of the chimney is cold because it has expanded due to lower atmospheric pressure. The air inside the chimney undergoes this exact same expansion, and loses the exact same temperature.
A fireplace chimney is different because the air at the bottom starts out hotter than the ambient temperature. When it comes out the top, it has cooled but is still hotter than the ambient temperature at that altitude.
I see what you're saying wrt the difference. Thank you.
The air once at the top wouldn't experience any expansion if it was the same density as the outside air, but what about the energy it picks up from expanding? Wouldn't it still have that? Of course it will have lost some from fighting gravity.
The chimney described here supports itself with the airflow it generates, which means it has to operate 24/7. That means it has to operate in stable air. It can't.
A fireplace chimney is different because the air at the bottom starts out hotter than the ambient temperature. When it comes out the top, it has cooled but is still hotter than the ambient temperature at that altitude.