This paper presents a numerical investigation of premixed methane/oxygen heterogeneous reaction characteristics in a micro-catalytic combustion chamber under various boundary and wall thermophysical conditions. A 3D model was simulated using ANSYS Fluent and validated against experimental data, with a maximum difference of only 1.92 % using a pure heterogeneous reaction. This study aims to analyze the wall boundary conditions and thermophysical factors that influence chemically and thermally during heterogeneous reactions. The results show that, with an increase in inlet velocity from 1 m/s to 10 m/s, the maximum heat produced by the reaction increases 52.67 % and the temperature of the channel as well as the outer wall increases accordingly. Using a 2.5 m/s inlet velocity, we found that the maximum external wall temperature uniformity coefficient was 0.1911. Furthermore, it was observed that as the heterogeneous reaction progresses, Platinum's surface coverage and the H(s) site coverage increase; however, the O(s), OH(s), CO(s), and C(s) site coverage decreases. Additionally, low convective heat transfer and wall thermal conductivity increase the efficiency of heterogeneous reactions and methane conversion. As a result of the low wall thermal conductivity, the outer wall temperature uniformity coefficient was 0.2863, while the methane conversion rate was 79.05 %. According to the results, higher thermal resistance increased the methane conversion rate from 68.18 % to 79.05 %, and the combustion process within the micro-catalytic combustor was uniform and controlled, thus enhancing its efficiency. The results of this study provide useful insights for optimizing micro-combustors, paving the way for future improvements in their design and operational efficiency.