Because slate is a natural stone, the heat and humidity normally associated with an attic will not harm the slate. Your problem appears to be one of cooling an upper floor area or finished attic space. Cold air is denser than warm air, and it is a challenge for the furnace blower to push the dense air any higher than one story. If your furnace fan is located in a basement or cellar of any two-story home, it will be difficult to cool the upper floors with just the one unit.
Solutions range from adding another unit for the second floor, to rearranging the ductwork to include a zoning system, to adding additional insulation to the attic area. The high cost of adding a zoning system often includes replacing the ductwork and the furnace and fan system because the fan will be required to work harder and longer. Adding a spray foam insulation to the underside of the roof slats (slate shingles often use slats in place of decking) will reduce the heat gain of the attic space. Because slate shingles are held in place with metal fasteners, some experienced roofers hesitate to recommend foam insulation. They are concerned that any possible moisture accumulation could cause the metal fasteners to prematurely fail. A sure solution would be to install a second cooling unit for the second floor or finished attic space. A second unit could be a window air conditioner or a split system unit, which uses a ground-based air conditioner and a window or wall-based fan system. No matter what you choose, make sure the finished area is well insulated to meet local standards and that the conditioned area is properly air sealed.
C. Dwight Barnett is a certified master inspector with the American Society of Home Inspectors. Reach him at d.Barnett@insightbb.com.