Our house has a covered back stairwell that was added after the house was built (I'm guessing in the 50's). The walls aren't insulated (just homasote in some places, drywall in others) and so it's very hot in the summer and cold in the winter. I'd like to simply just tack some polystyrene board and then cover it all with drywall but I'm not sure if this is a good idea (especially drywall-poly-drywall) or an incredibly dumb one.
Rookie ~ Chicago, Illinois
In order for your home's stairwell to maintain a comfortable temperature year round, you will need to install some type of insulating material into the walls and ceiling, as well as provide a heat source. (Once the stairwell is well insulated, it might remain adequately comfortable during the summer months even without air conditioning). Although I know of no reason why you couldn't hang sheets of solid insulating board over the existing interior wall covering, I'm not convinced that this is the best way to solve your problem.
Most brands of extruded polystyrene have an insulating value of about R-5, per 1-inch of board thickness, which means that you might achieve an R-10 insulation value with some 2-inch board. Yet that minimal addition in insulating value might cost you some valuable space within your home's stairwell. Perhaps a better option would be to install some blown-in insulation into the wall cavity behind the existing interior walls. Depending on the depth of the wall cavity, you might achieve an insulating value of R-19, without having to give up any stairwell space or hang new sheet rock. The new insulation could be blown into the wall cavity through small holes in the drywall, which would then be patched and refinished.
If the existing interior walls are in poor condition, then you may also consider the option of just tearing out the old drywall, insulating the wall cavity, adding a proper vapor barrier and hanging a new finished wall. Of course this option may involve more work and cost more, but at least the job would be done right.