The onset of the unstable temperature distribution which may appear in plane axisymmetric catalytic burner is studied. The instability mechanism is assumed to be related with the temperature dependence of the viscosity, thus with the pressure drop in the porous combustor, governed by Darcy's law. An area e.g., of lower temperature (dark zone) characterised by a smaller value of the kinetic viscosity gives rise to a locally increased gas flow mass velocity, the pressure drop remaining constant over the burner cross-section. The locally increased mass velocity produces an enhanced cooling of the area, whereby heat conduction from the hotter surrounding area tends to restore a homogeneous temperature distribution. A linear analysis of this thermal instability mechanism is carried out and yields a simple analytic solution for the state of neutral stability. (C) 2003 Elsevier Ltd. All rights reserved.