You could try covering the lid with foil. I took cardboard and made a lid cover that fits with the screen. I cut a window out to allow the light/heat to pass through. I then covered the cardboard with foil. I did it this way just in case I need to take it off during different seasons I can just take it off. This would prob work for you since you place damp rags on your lid. The foil will help keep your heat in and humidty for that matter. You may not need two anymore. Another thing many use is foil tape to cover the screen as needed. This is alittle more permanent and wont allow you to place the rags on the screen.