Our house is a one level bungalow/rancher with an unconditioned attic.  I’ve been gradually doing things to improve air tightness and was considering an airtight chimney cap — the spring loaded ones that close by a chain that dangles down to the firebox seemed interesting.

In winter, would this mean that there is a danger of condensation inside the chimney? 

In trying to think about the building science, I suspect I’m overthinking it.  The chimney is probably just a bad thing to have with respect to insulation and air tightness (because you don’t insulate it and it’s extra work to make airtight.

However, I don’t want to cause a mold problem.

Climate zone 4