A mansard roof is distinctive in that it extends down vertically, sometimes enough to cover windows on the floor below. Its design means that it is difficult to insulate because it only has a small amount of attic space. As well as being insulated, the area also needs to be protected against damp so that the wood does not rot.
Drill a series of access holes into the roof space. As a mansard roof extends vertically down the building, these holes are drilled into the walls. The holes need to be drilled in a space between the joists in a vertical line about a foot apart. You will need to pour the insulation foam through these holes. Pouring foam insulation comes in can form with a nozzle attachment.
Place the nozzle of the foam insulation gun into a hole at the bottom of the roof and depress the trigger for about 20 seconds. Remove the nozzle and stuff the hole with a rag to prevent the insulation escaping when it expands. Move up to the next hole and repeat the process, pouring foam and plugging the holes as you go. When you have poured insulation into the hole at the top of the roof, leave this one unplugged. This is to release any pressure that may build up. When the insulation has expanded and hardened, remove the rags and repair the holes in the walls with filler. At this point, cut away any insulation that may have escaped from the hole at the top that you left unplugged and make the surface smooth. You may need to use filler to do this.
Attach the vapour barrier to the inside of the attic roof by cutting the sheet into strips to lay it between the rafters and staple into place. This attaches the vapour sheet to the part of the roof that extends down and forms the walls of the room and as this will probably be unattractive, you may prefer to install this layer under the floorboards of the attic room instead
Apply the caulk to the edges where the vapour sheet meets the edge of the roof.
Insulating a mansard roof is a difficult, time consuming process, and unless you are experienced in home maintenance, you might want to consider hiring the help of a professional.