I'm in a land of temperature extremes, with a room full of tanks. I heat it with a dehumidifier. The baseboard electric heating never comes on, but the dehumidifier costs to run. The room is well insulated, and tight.
Frankly, humidity is a big reason I changed what fish I keep. I now aim for species happy at 22 or so. Even a bit lower is good. The room is built into a large, unheated garage, so it doesn't affect the house, but I don't want it to be destroyed or unhealthy to be in.
I have never done a fishless cycle. If you have to run the tank at 28, you are guaranteed massive evaporation, but it should moderate once the tank is at a sensible level. I think you have a temporary problem there.
With the changes in our leisure approaches, fishless cycles suddenly matter. In the past, you'd connect with someone in an aquarium club and they'd cycle your filter media for you, with no fussing or water droplets on the lid. The loss of the human side of the hobby has repercussions.