My suggestion is to call your local gun dealer and ask if they sell desiccant packages. These are the things you find in the shoe boxes at the local WalMart. It is a moisture absorbant and should help. When I worked retail I used to collect them rather than throw them out and I would toss them in my gun safe to help keep the moisture out.
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I've read about a lot of successes with the rice trick, but my sister tried it and discovered it made quite a mess with the rice dust. SO, if you use the rice make sure you just set the device on top of the rice in the bag and not down into the rice.