I want to be compensated for my outrageous light bills

More details are needed. Do you own or rent? Have you reported the issue to the electric company? What was the result of having the furnace checked? If you rent, have you made a written request to the landlord to have the issue checked out? Have you checked the insulation in the house? You never describe the cause of the issue. You let this go on for a very long time. If you own the house, I don't think you have claims against anyone unless there was a cover up of this issue by the seller or if the issue was caused by a faulty system that you purchased. Your claims would be against the manufacturer and may be covered by a warranty.  If you rent, this has been going on a long time. If you have never notified the landlord, I dont think you can get your money back from anyone. You need to notify the landlord as soon as possible.  Either way, whoever you try to sue will allege that you failed to mitigate your damages by letting this go on so long.  This is probably too complicated of an issue to get an adequate answer on a general legal advice forum. Contact a local attorney for specific advice.