Alternating electric fields (e.g., TTFields) may be applied to a subject's body using electrode assemblies, each of which includes a plurality of graphite sheets (or sheets of another conductive anisotropic material) that are positioned adjacent to, but not touching, each other. One or more electrode elements are disposed in electrical contact with each of the graphite sheets. Strips of electrically insulating and thermally conductive material are disposed between the graphite sheets, and these strips are positioned in thermal contact with the adjacent graphite sheets. The graphite sheets facilitate the passive spreading of heat within the confines of any given sheet. And the strips of material allow the passive spreading of heat to continue beyond the confines of any given sheet without compromising inter-sheet electrical isolation.