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 reactive mixture is divided into the pre-flame, reaction, and post-flame zones. Then, 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.