Lots of people use an old fridge with a small light bulb in it. I have a much smaller RV that holds enough rod for my limited stick work. A vent that can be adjusted would be a good idea. It doesn't take much of a bulb to heat a rod heater box, mine has a Christmas tree bulb in it,, the old style.
As to the importance of dry rod just because it lays a bead does not mean its a sound weld. Some rods lose nothing when damp 6010, 11 and 13 would be examples. Others, most notably the 7018, 8018 and 11018 types lose important properties when damp. Other types will lose flux when damp. The people who manufacture the rods is my guide as to whether it is important to keep thier rods dry,,,