Birchwood Casey Sheath & silicone sock... just like poster Elde stated!

Then I would buy two bags of charcoal for cooking - lay them on top of the gun case & slice both bags from top to bottom with a knife -- then lay the sliced sides face-up on top of the case that holds these guns. Charcoal draws moisture like it's nobody's business. It will act a humidity shield for that case - if by-chancea few mornings get below freezing or extra wet.

Should then be good-to-go for Arizona climate.