This Brief reviews contemporary research conducted in university and industry laboratories on thermal management in electrochemical energy storage systems (capacitors and batteries) that have been widely used as power sources in many practical applications, such as automobiles, hybrid transport, renewable energy installations, power backup and electronic devices. Placing a particular emphasis on supercapacitors, the authors discuss how supercapacitors, or ultra capacitors, are complementing and  replacing, batteries because of their faster power delivery, longer life cycle and higher coulombic efficiency, while providing higher energy density than conventional electrolytic capacitors. Recent advances in both macro- and micro capacitor technologies are covered. The work facilitates systematic understanding of thermal transport in such devices that can help develop better power management systems.