I'm unable to vent out through the side wall so I need to go through the ceiling. There is about 10" of ceiling space and then above that the unconditioned space just below the flat roof. it's heated a bit by the house but it's mostly open to the cold winter through its vents and a gap in the side. What r value would be enough to sleeve a kitchen 7" vent to stop condensation? R8 doesn't seem like enough. The exit will go into the soffit area and then down so it's exhausting to outside air

The previous owners of my house added a single room 300 sqft extension off of the side. Its on slab and its conditioned by ac and a hydroair system that is beyond overkill for the small space. Now, entering my third winter in this house (and being home more often), I am ready to tackle the leaky air that keeps the room so cold. Some of the facts: [list] [*]The blower is in an unconditioned utility closet that shares a wall with the room and is accessible from the outside. I have sealed up every crack of that closet and ensured the duct work that is exposed in the closet is insulated fully. The duct work goes up into the ceiling, which I cannot access. [*] [*]A master bath was installed above this extension room, it is also pretty chilly in the winter. [*]On the coldest days, will need to cycle every hour to keep temperature (with a 3 degree delta set on the stat) [*] [*]three 3x12" supplies in the ceiling, one larger return in wall near ceiling (maybe 10x20") [*] [*]The room is currently 62F. Outside is currently 45F. I borrowed a FLIR gun and found several spots that are 50F along the baseboards, in corners, and around the sliding door. The registers and return all read about 60F. [/list] Based on the FLIR readings, it doesn't seem like cold air is leaking in (maybe I need to remeasure on a colder day) from the HVAC ducts..?? Do the 50F spots along the baseboard maybe explain it? If so, any suggestions on sealing them up?