Abstract: The invention is a catalytic air cleaner made from a double spiral formed by winding together two strips of metal. The strips are coated with a combustion catalyst. One spiral passage leads into the core of the spiral and the other passage leads out of the core. An electric resistance heater supplies heat at the core of the spiral. The outflowing air transfers this heat to the inflowing air, through the walls of the spiral. Because of this heat exchange, the difference between the temperature of the air at the core and the air entering the spiral can be many times the difference between the temperature of the air entering and leaving the spiral. Contaminants in the air are burned on the catalytic surface with a minimum input of heat. The invention also includes a method of designing a spiral having optimum characteristics.