A system to convert electric power into methane includes a reactor having a first chamber and a second chamber separated by a proton permeable barrier. The first chamber includes a passage between an inlet and an outlet containing at least a porous electrically conductive cathode, a culture comprising living methanogenic microorganisms, and water. The second chamber includes at least an anode. The reactor has an operating state wherein the culture is maintained at a temperature above 50° C. The system also includes a source of electricity coupled to the anode and the cathode, and a supply of carbon dioxide coupled to the first chamber. The outlet of the system receives methane from the first chamber.