I live just down the road from Houston. I have a large safe with a Goldenrod heater. It has been running for over 5 years. I pull the residents of the safe a couple times a year and inspect, oil or grease as needed. RH in the room is usually about 40-50%, but the small amount of heat in the safe seems to be adequate to prevent rust. Long term storage items get a coat of Rig grease inside and out, my favorites get used, and oiled after use, then again a few days later. All stored muzzle down. Works for me.
As a side note, a few years ago while searching for something on the web I ended up at an engineering site discussing corrosion. One of the things I remembered was it discussed was the corrosion (rust) formation rate of metals, and one section specialized in steel. If you can keep the RH at 50% or less, it greatly reduces the rate of rust formation. It does not stop it, but since the reaction rate is an exponential function of the water vapor concentration, it greatly slows it down the lower the humidity.