They make those Golden Rods, Dri Rods and other brands of gun safe heaters in different sizes.
They add enough heat to the safe to keep moisture from forming.
Add one to your safe. I would be concerned with the location of the safe. As stated above, it will be the same temperature in the safe as in the room where it is, without some kind of a heater.
I would probably go with an 18 inch or a 24 inch model. It will cost much less to run than trying to heat the whole area where your safe is located.
I put the heaters toward the bottom of the safe, or on the bottom.
I do not think that I would try to seal the door. Most safes are not airtight, and some air has to move through the safe.
I have seen many firearms that were kept in a unheated area, and the results are not pretty.

I see that Noah posted about the same time that I did. He is absolutely correct. A light bulb set up like he suggests will work very well also.