It's Science folks.
Air can only hold so much water before it condenses out.
That temperature is know as Dew Point. Go outside in the morning to find the Dew before it hides
If you heat the air inside the safe the RH drops. It's not driven out of the safe. Warm air can hold more water vapor than cold air thus the Relative Humidity drops. The Dew Point stays the same, the water is still there, but the warm air has more degrees of cushion before the water vapor condenses. For example, a Dew Point of 40 degrees can have 100% RH if the temperature drops to 40 degrees, but be relatively DRY if the ambient temperature 60 degrees.
A Dew point of 60 degrees will condense out at 60 degrees but be relatively dry (RH) @ 80 degrees.
Long Term storage of metals, untreated wood, paper, or Cigars at RH of over 70% accelerates oxidation (excess water vapor will combine with surface contamination).
A somewhat sealed safe has a lag or delay from outside conditions. As temperature drops the seals and mass of the safe stays warmer (Good). Overnight the temperature inside and outside will equalize. Depending on the Dew Point that may be OK. But that lag will keep the interior of the safe cold longer as the outside air warms up. Still OK if the safe did not reach the Dew Point during the night. Dew forms almost everywhere, even on Cacti.
Adjust your heater wattage to give you 10 to 20 degrees warmth, above ambient inside your safe.
If it has a thermostat pick a temperature above your seasonal Dew Point.
How many use a 100 watt bulb in their pumphouse to keep the pipes from freezing?
50 to 100 watts (1/2 to 1 amp@120 volts) should be plenty for a 'Large' safe. Most of the electric safe Dehumidifiers are less than 20 watts and good for a 'Small' safe.
Absorbers absord mositure, a cold safe sucks in more damp air and the absorber collects more water vapor. Moisture absorbers are good at keeping the RH levels below 70% by sucking up water but over time they can saturate, gain water weight and stop protecting. Most absorbent materials have a known max water content that can be checked by weight.
