You know, don’t let my comments discourage you from trying what you want to do. But perhaps a white umbrella would be a good start.
I’ve been perusing that solarcooking.org site. Good Ideas. There’s one that can fold down into a 9″x12″x2″ bundle, made of cardboard and foil. Perhaps that, or something sized appropriately, could fit behind a sleeping pad that is being used as the structure for a frameless bag.
The site keeps referring to using a black pot inside of a plastic bag, to capture and retain the heat.
Another option would be an aluminum pop can, painted black on the outside, lowered down into a Nalgene bottle. Nalgene can withstand temperatures of 200F.
Another one uses a reflective auto windshield screen. That could go behind the sleeping pad too.
Thanks for getting me thinking.
Dwight