According to various aspects of the present disclosure, exemplary embodiments include assemblies and methods for dissipating heat from an electronic device by a thermally-conducting heat path to the external casing via one or more portions of an electromagnetic interference shield and/or thermal interface material disposed around the device's battery or other power source. In an exemplary embodiment, a thermally conductive structure which comprises elastomer may be disposed about or define a battery area such that heat may be transferred to the external casing by a thermally-conductive heat path around the battery area through or along the thermally conductive structure which comprises elastomer.