A thermal conductor for use with an electrochemical energy storage device is disclosed. The thermal conductor is attached to one or both of the anode and cathode contacts of an electrochemical cell. A resilient portion of the conductor varies in height or position to maintain contact between the conductor and an adjacent wall structure of a containment vessel in response to relative movement between the conductor and the wall structure. The thermal conductor conducts current into and out of the electrochemical cell and conducts thermal energy between the electrochemical cell and thermally conductive and electrically resistive material disposed between the conductor and the wall structure. The thermal conductor may be fabricated to include a resilient portion having one of a substantially C-shaped, double C-shaped, Z-shaped, V-shaped, O-shaped, S-shaped, or finger-shaped cross-section. An elastomeric spring element may be configured so as to be captured by the resilient conductor for purposes of enhancing the functionality of the thermal conductor. The spring element may include a protrusion that provides electrical insulation between the spring conductor and a spring conductor of an adjacently disposed electrochemical cell in the presence of relative movement between the cells and the wall structure. The thermal conductor may also be fabricated from a sheet of electrically conductive material and affixed to the contacts of a number of electrochemical cells.