In this study, a steady state analytical investigation of conjugate heat transfer in a planar micro-combustor is presented by considering the detailed reaction mechanisms for a methane/air mixture with 10% and 20% hydrogen addition. The primary objective is studying the effects of hydrogen addition on the wall and gas temperature distribution in order to propose a practical solution to manage the significant heat transfer in micro-combustors. The conservation equations are analytically solved in each zone using the matching conditions. Moreover, to present a general analysis, appropriate non-dimensional thermal parameters are recommended considering the thermal interaction between the reactive mixture, solid structure and ambient. As a result, appropriate correlations for the normalized wall temperature profile are presented for different situations that can be used as a prescribed wall temperature distribution in numerical simulations. Moreover, it is found that for the cases with solid-fluid thermal diffusion ratio greater than 50, the thermal properties can negate the effect of hydrogen addition on the wall temperature distribution. (C) 2020 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.