Here's a thought for the underside.
Take an inflatable matress, on top of it put a layer of the white fiberglass batts. Maybe use some high temp resistant duct tape to hold them together/to the matress. Drive car over, inflate. This should do a pretty decent job of closing off all the air gaps.
Also insulate the firewall as best possible as this would be the one area that heat could still escape from.
It would seem to me that a properly designed front clip sleeping bag would do a very good job of keeping things toasty.
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