No, you as a landlord have to provide them with heat. They shouldn't have to spend their money for the electricity to run the space heaters, get over it.....
What a doosey of a predicament for both sides. Well, in a nut shell I have to say yes they are being unreasonable since it seems that you are doing everything you can think of for them. You've provided the space heaters and if they choose not to use them that is their own concern. Try to ease their stress by reassuring them that you have their best interests at heart and are doing all you can for them. These people are expecting you to fix it today like you have a money tree in your back yard so you also need to inform them that this is a very big and expensive job. But do get this done within a reasonable time frame. DO NOT explain that you have no money or anything like that. Because you should always be prepared for an emergency.. Most of us are not prepared however and this causes a predicament like the one your having now. Make your comments simple and polite. Continue to bring wood and invite them for a homemade dinner one night at your house. You could also bring over some extra blankets.... they should be appreciate and this will hopefully remedy your problem.