The conductivity of electrolytes in high temperature fuel cells increases with increasing temperature. It is shown that this property may lead to instabilities, inhomogeneous temperature fields, and hot spots. A simple spatially one-dimensional model of a cell is studied by phase plane analysis and numerical bifurcation analysis. The operation of the cell at constant voltage and at constant current is considered. It is found that in both cases spatial temperature patterns and channels of high current density can form. (C) 2004 Elsevier Ltd. All rights reserved.