I did it in preparation for a March trip to Alaska. It definitely made a difference.
I used the Owens Corning Pink Foamular panels and covered all of the interior surfaces including the "top" or "ceiling" as it were of the compartment AND the compartment doors. This stuff is water resistant so moisture is not a big factor. I coverd over the insulation with plastic Coroplast panels that are smooth and will Protect the foam insulation.
It is well worth it and it keeps the bed warmer. And yes depending on the temperature you can lose a great deal of body heat through the mattress if it sits on something cold.