My gun cabinet is in the garage (non-air conditioned), hidden away behind a sheet of plywood. And I'm in north-east Florida, not exactly known for its lack of humidity. Plus, I'm about a mile from the ocean.
For the two years I've had the cabinet in the garage, I've burned a 20-watt bulb on the floor of the cabinet, set in a small lamp base. That keeps the cabinet warm, allows no condensation to form, and I've never seen a spot of rust on anything. I check every few weeks, and give a quick wipe over with an oily rag. But so far, touch wood, it works a treat.