All guns face the possibility of rust due to moisture inside an enclosed environment.
I believe the safe that you are talking about is a steel unit, and not a fire rated unit. Fire rated units are more prone to moisture build up due to the insulation. Although your unit does not have that insulation, it still lacks air circulation, and can still have internal moisture build up.
You could buy an inexpensive canister of silica gel and place it inside your unit to make sure that the moisture never got out of control. If you wanted to get fancy, you could install an electric dry-rod device. The dry-rods are not a dehumidifier, but simply a device similar to a light bulb. A filiment produces heat, which keeps the interior of the safe warmer than the exterior, forcing the moisture to the outside.