I have a Thermic boot dryer which uses warm air, but nowhere near enough to effect my footbeds. Regardless, I never keep it on for more than a couple of hours - there's no need and if my boots aren't completely dry, they will be by the next day.
However, I have learned to be careful with my Hotronics as they they get pretty hot when set on 4. While I rarely turn them up to 3 when I'm wearing my boots, I (used to) crank them all the way up to drain the betteries before recharging.
Got new boots last year and both the fitter and I were surprised to see the toes of my Instaprint footbeds deformed. Nothing a little zap with a heat gun couldn't fix, but no longer use the 4 setting.