Just a little heat works. All it takes is a couple of degrees above the room temperature. A piano drier, a reptile warmer rock, small light bulb, or similar small heat producing item placed at the bottom, inside the cabinet, will keep it dry.
In any case, I would run it without the gear in it for a day or so and make sure it does not get too hot inside.
You might be able to find a food dehydrator for less than one intended for photo equipment, though as with the hair dryer I'd make sure it can be set to a low-enough temperature.
The other old standby is to put the gear in a sealed container with a large amount of uncooked white rice (or silica-gel packs).
Most decent hairdryers have a few settings on them for both level of heat and fan speed.
Still way too hot. The lowest setting for a hair dryer is still several hundred watts, and the required power, while dependent on the cabinet, is certainly less than about 40 watts as a maximum. In any case, anything greater will incur a pretty large operating expense. A 40W source, operated continuously, costs about $40 per year.
Reptile heat pad, under $15. Available in sizes from 7 to 25 watts or so. They are designed to keep reptile enclosures 7 to 10 degrees above room temperature. Plus, no noise.