AFAIK it also conducts heat very well. That is the same mechanism that you can see if you put a pot filled with hot water on snow or cold floor. While the pot may reflect some heat inside, it will still get cold fast. If you have an Airbed around the pot it will hold the heat much longer. So I don't think the blanket does a lot for you.
Another reason to start with the mat is that it is the cheapest to fix. WHile down jacket are of course very nice, a foam pad has an unbeatable price and is a good place to start looking where the cold is coming from.