[Christ]

Do the test. Then think about what you're saying.

In order for heat to radiate effectively, there has to be a differential between the area that is heated, and the area that is being heated. Hence the term radiation.

We know from physics that everything will follow the path of least resistance, which in this case, is the area with the largest temperature differential.

The heat is actually radiating OFF the roof, into the open air. The headliner is there so you can't touch the hot roof, it's there for aesthetics, and for sound insulation. It's not there for temperature insulation. (Cardboard is crappy insulation anyway.)