Headliner install

You definitely want something there to insulate temperatures and noise, rain drops on a steel roof can be deafening, the stick on or spray adhesive for non stick type. I think most vendors that sell headliner also sell the factory fiberglass like type that is probably all you need. I imagine the cardboard is an insulating material itself seeing how you found no additional under it so anything you put in there will be an upgrade.
I have some other areas in the car that need some insulation, so I'll be sure to get enough to do it all.

Thanks!