Well, Jesse- remember that the spontaneous combustion temp of wood is about 800 degrees. Wood smolders at 700 degrees F. So don't worry about the temp. But I know it still feels dangerous, I have a hot box, similar to yours, with light bulbs for heat. I get worried when the temp gets up to 120. Really, what I have read is that 25 degrees above ambient is enough to dry wood. 180 degrees is more like what a lumber kiln operates at. But I have good luck running at 100 degrees. If you are drying wet wood make sure the wet air can flow out.
Probably more houses or shops burn because of bad electrical wiring, so make sure you don't cut any corners there.