We have a gas dryer but don't like shrunken clothes. During the winter we hang them in the same room with our (innefficient) furnace. They dry relatively quickly with nothing more. There is no air-flow. As for the humidity, we don't have to run the dehumidifier in the winter - it stays nice and dry there. In the summer, likely because of our climate, we have to run the dehumidifier to keep the basement from getting damp. But then the clothes are hung outside. I suggest trying it by hanging them in the furnace room (just keep them well away from the furnace and any sources of ignition). See what happens. It won't cost you anything.