The electrical. (ionic) conductivity of polymer electrolytes for lithium-polymer cells increases greatly with increasing temperature (in contrast to the thermal conductivity). This paper examines, by both a Linear perturbation analysis and by numerical calculation, an instability that could arise from this temperature dependence. The instability is one where a local perturbation to a higher temperature results in higher electrical conductivity and therefore the passage of more current in this region with an attendant increase in heat generation. If this excess heat generation cannot be conduced into adjacent cooler regions, instability (growth of the perturbation) results. The numerical calculations were carried out for constant potential drop across the electrolyte, for constant mean current density, and for constant mean power discharge schedules. The calculations suggest that this instability is unlikely for small batteries (of the order of 0.1 m in the directions parallel to the electrodes) but may occur for larger batteries such as those intended for use in an electric vehicle. However, the growth rates of the perturbations do not appear to be high. Changes in cell materials /thickness have little effect on the instability. The Linear perturbation analysis is in approximate agreement with the numerical calculations.