The present disclosure is directed towards the design of bipolar plates for use in conduction-cooled electrochemical cells. Heat generated during the operation of the cell is removed from the active area of the cell to the periphery of the cell via the one or more bipolar plates in the cell. The one or more bipolar plates are configured to function as heat sinks to collect heat from the active area of the cell and to conduct the heat to the periphery of the plate where the heat is removed by traditional heat transfer means. The boundary of the one or more bipolar plates can be provided with heat dissipation structures to facilitate removal of heat from the plates. To function as effective heat sinks, the thickness of the one or more bipolar plates can be determined based on the rate of heat generation in the cell during operation, the thermal conductivity (“k”) of the material selected to form the plate, and the desired temperature gradient in a direction orthogonal to the plate (“ΔT”).