Methane consumption is strongly increasing as a result of its abundance from natural gas, thus leading to reduced costs, and as a result of the reduced environmental impact in the case of combustion, with a lower carbon content with respect to traditional fuels. These advantages encourage its utilization in several industrial applications, such as methane steam reforming for the production of hydrogen and automotive applications. The necessity of transporting the gases and large-scale distribution systems is however one of the main issues. Innovative processes, such as cryogenic storage, cryo-compression, and liquefaction, require detailed information on the thermal and chemical properties of the methane hydrogen mixture at low and ultralow temperatures. In this framework, detailed kinetic models for the total and partial oxidation of methane, hydrogen, and methane hydrogen mixtures in air at low (273 > T > 200 K) and ultralow (T < 200 K) temperatures must be developed and validated. In this work, the laminar burning velocity of these gases has been simulated and compared to the few available experimental data retrieved from the literature. Hence, simplified correlations for the burning velocity with respect to the initial composition and temperature have been adopted and further developed. The simplified approach proposed in this work reduces the number of degrees of freedom required for the application of the modified Gulder equation. Moreover, it is suitable for the description of the combined effect of the initial temperature and gaseous composition. The performed analysis of the concentration and temperature profiles with respect to burner head distance indicates, as a possible explanation for the methane-dominated regime, the presence of a limitation in the hydrogen concentration hindering its production. A sensitivity analysis was performed to evaluate the effect of hydrogen addition and initial temperature on the methane kinetic mechanism in the presence of air. The results show that, although the hydrogen production rate does not change, the reaction mechanism is strongly affected by the studied parameters.