Tenchi23 said:

Tape a piece of foil, a layer of paper towel, plus a piece of cardboard (in that order) to the outside top of your shot gun box. This will prevent moisture accumulation on the inside of your lid.

The explanation is long,and verbos. It has to to with how condensation functions between two environments of disparate temperatures that have come into contact with one another. In this case, warm shotgun box vs slightly cooler room temp.

For the my fellow geeks, here's a link that gives a more complete explanation:
http://www.insulationstop.com/radiant-barrier-blog/how-to-reduce-condensation-with-reflective-aluminum-foil-insulation/

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