If there is higher-than-normal energy costs due to the landlord's failure to maintain or replace appliances, then the landlord may be liable for that extra cost, since it is due to her negligence and breach of her obligation as a landlord to keep the rental premises utilities in good working order. That is the theoretical answer. Practically, as someone who has had several similar cases, I can tell you that unless the landord chooses to voluntarily compensate you, it is very difficult to get compensation from the courts. You have to be able to *prove* both the reason for the high costs and what the costs would have been in the absence of the problems, which generally takes immensely detailed paperwork (e.g. energy bills over a period of time), reports from electricians, the utility, or contractors who are knowledgeable about and inspect the appliances, and possibly testimony from one or more electricians, etc. Courts will not just infer that some problem causes higher costs; you have to prove it by a preponderance of the evidence.