With high efficiency and small thermally-induced effects in the near-infrared wavelength region, a diode-pumped alkali laser (DPAL) is regarded as combining the major advantages of solid-state lasers and gas-state lasers and obviating their main disadvantages at the same time. Studying the temperature distribution in the cross-section of an alkali-vapor cell is critical to realize high-powered DPAL systems for both static and flowing states. In this report, a theoretical algorithm has been built to investigate the features of a flowing-gas DPAL system by uniting procedures in kinetics, heat transfer, and fluid dynamic together. The thermal features and output characteristics have been simultaneously obtained for different gas velocities. The results have demonstrated the great potential of DPALs in the extremely high-powered laser operation.