Heat bulbs will fry your humidity, it's very hard to compensate. You could 1) cover up more of the lid 2) have a giant water bowl under the heat lamp so evaporation increases 3) add a second water bowl 4) keep spraying like its your job.

If you can do a radiant heat panel it will be better on your humidity. Otherwise, in the day or two before he sheds just spray the heck out of everything.

JonV