The Sentry and similar home/office fire proof safes use a layer of high density water impregnated foam between the steel of the walls. So yes, the relative humidity inside the safe when closed does get high. If you are going to use one of those, you would be wise to take some measures to protect the weapon. Either be sure to keep it regularly wiped down with CLP or some other rust inhibiting oil, or use a bore sock or something similar.
Personally, I'd prefer just a security safe for firearms, not a fire proof one.