I recommend that you check with your town hall about the permit situation. It is always a good idea to make sure you have a permit if one is required. If a permit is required and you don't get one, it could hurt later on down the road (if the house gets reassessed, you go to sell, etc). When you check about the permit you can find out about what would lead to an increase in taxes. If adding the room is going to add to your taxes I think you should add heat. If adding heat is what will cause the room to be taxed, that is something that you will have to decide if you are willing to do.
Realty Executives, Pequannock