There is jute padding that is glued to the roof. You can buy this stuff by the yard in various thicknesses at many fabric stores for a fraction of the cost of what a restoration supplier would charge. You can mail order it as well in rolls.
When you glue it in, I recommend a spray by 3M called yellow super trim adhesive. They come in numbers with the higher number being higher adhesive bond. Just cut pad to fit between metal ribbing, spray both the roof and the pad separate and allow to dry a few minutes, then stick in place. That stuff is amazing. I use it on lots of stuff and it is strong like construction adhesive. Just make sure of placement before you stick in place.