Square box insulation shield with inside insulation?

Finally got all the chimney parts. 6" Dura tech, the square ceiling box is 36" high and will go from the ceiling up to the roof.
Question is: should we insulate around the pipe inside that black box and cap it shut around the pipe at the roof line under the flashing? There is a min of 2" space more in the corners.
Any thoughts on this?

 

I was thinking of hi temp ceramic insulation. Does that make sense?

 

I'm not 100% visualizing it but if it's what I think then no don't. I believe there's air space in there for a reason. If you jam it full of insulation and cap it off then you aren't using it as it's designed.

Follow the instructions to a T

 

Thanks Babaganoosh. Yes, i think you got the idea and are probably right. Just thought it might help the draft but i'll leave it alone.