Understanding and improving the performance of miniature devices powered by micro-combustion have been the focus of continued attention of researchers recently. The goal of the present work is to investigate the behavior of premixed methane–air combustion in a quartz microreactor with an externally controlled wall temperature. Specifically, the impacts of the flow inlet velocity, the equivalence ratio, and the microreactor channel size are examined. This study is conducted by means of computational simulations, and the results are validated against prior experimental data, as well as by other similar studies in the literature. Utilizing simulation results with detailed chemistry, the present work provides more in-depth insight into a variety of phenomena, such as ignition, flame propagation, flames with repetitive extinctions and ignitions (FREI), and flame stabilization. In particular, the ignition, the flame span, and the FREI-related characteristics are scrutinized to understand the underlying physics of the flame stability/instability modes. It is shown that the flames appear stable at higher inlet velocities, while the FREI mode is detected at a lower inlet velocity, depending on the equivalence ratio and the channel size. The findings also explain how different operating conditions impact the flame characteristics in both stability modes.