Off the top of my bald head, I'd put the thing in a heavy duty plastic bag, and almost seal it. By almost I mean put in a few pin pricks...this allows the humidity to change slowly, and any rapid change and the humidity condenses on the outside of the plastic.

Variations of this idea are used to cure green wood, for example you dig up a walnut stump and want to use parts of it for gun stocks etc. you seal it in plastic and leave a few small holes. In that case there are a few more, you are trying to get it to 'average moisture content' so as to not allow it to check in drying.

The second comes from the best way to store electronic gear in the sub arctic, which in winter, one uses plastic bags for laptops, which are sealed. It's not uncommon to have a temperature range from indoors to outdoors of over 80C and without the bags things like cameras and lenses are..well...full of condensation.

John Conley
Musica est vita