Insulated ceiling within chase

[ShenKen]

New construction here, wood stove in basement with the chimney pipe coming up through the interior of the main floor. At the second floor it goes through an insulated chase that is built onto the side of a dormer, so here it is technically still in the interior of the envelope. Planning no insulation (just drywall) between the finished dormer and the chase so as to let a little heat come into the dormer from the chimney pipe. I'll attach a photo taken from inside the dormer.

It seems to me that, to stop heat loss from the interior, there should be an insulated "ceiling" somewhere in this chase, maybe approximately in line with the second floor dormer ceiling. I could frame it with 2x4s or 2x6s and on the underside install a fire stop to keep the pipe spaced properly, and a layer of drywall to keep the insulation up. Metal-Fab offers an insulation shield that would slip over the pipe and attach down to the framing directly above the fire stop. Metal-Fab says this insulation shield is not needed in an enclosed chase but I'm not sure if their assumption is that there will be no insulation.

So my question: do I need the insulation shield, or can I just lay rockwool around and up against the pipe within the chase?

Chimney pipe being used: Metal-Fab Temp Guard TG Max.

Interior dimensions of chase: 22"x27".

Photo taken from inside second floor dormer and shows chase with chimney pipe entering, and fire stop and insulation shield in foreground.

 

[begreen]

There needs to be a firestop at each floor intersection. Insulation is not supposed to be up against the chimney pipe. If the exterior walls of the chase are insulated, then a ventilation grille could be installed at the top and bottom of the interior chase drywall to facilitate warm air convection from the chase into the room.