Wow,that's weird,sounds like more of a problem then just the heat going on...it's like 25 here in NY,my heat is on and my tanks are actually right against the wall where I have the heat,but I have a spacey living room and it's connected to the kitchen so it's not affecting my humidity a whole lot.i have aspen in one tank and coco husk in the other.
where is your tank located and where is your heat located? Do u have this tank in a smaller type room?
I'd say keep 80% of the top of the tank covered with wett,not damp a wet towel. I keep my towel extremely wet..my tank stays a round 86 give or take hot side ,a hot spot of 91 and humidity stay steady between 40&60 on avg,as long as I mist a 1-2 times a day and keep most all of the screen covered with a wet towel