Minimising the thermal gradients is extremely important in a planar solid oxide fuel cell (SOFC) for improving the cell life. The estimation of the temperature distribution in the cell is necessary to achieve this objective through suitable control, since they are not generally measurable. In this work, we have designed a non-linear adaptive observer for estimating the temperatures inside the hydrogen fed planar SOFC. The observer design is based on a lumped parameter model of the SOFC. The stability of the proposed observer is proven using the Lyapunov function method and is based on the concept of input-to-state stability for cascaded systems. The simulations show that the developed observer can track the temperature and species concentration profiles in the planar SOFC during step changes in the cell current. The adaptive observer presented is valid for a wide operating range, requires fewer variables to be measured, and is robust to fluctuations in the inlet flows. (C) 2012 Elsevier Ltd. All rights reserved.