This work focuses on the thermal management of a monolithic reactor for catalytic combustion of methane at pressure relevant to gas turbine applications. The role of operating pressure on methane conversion, temperature profiles, and relevance of homogeneous reaction with respect to heterogeneous reaction is investigated both experimentally and numerically. Experiments of self-sustained methane combustion over a 20 wt% LaMnO3/La-gamma Al2O3 monolith are performed in a lab-scale test rig with operating pressure varying in the range of 1-12 bar. A Computational Fluid Dynamics (CFD) model simulating a 10 x 10 channel configuration is also developed to carry out a parameter investigation. Numerical results have allowed the identification of a reactor configuration in which only the outer perimeter channels of the monolith are coated by the catalyst, thus activating methane reaction. In the central region, that is not catalyst-coated, methane conversion by homogeneous reaction is made possible by the radial heat transfer from the external catalytic channels through the monolith walls. (C) 2012 Elsevier B.V. All rights reserved.