In recent years, a diode-pumped alkali laser (DPAL) has become one of the most hopeful candidates to achieve the high power performance. A series of models have been established to analyze the DPAL's kinetic process and most of them were based on the algorithms in which only the ideal 3-level system was considered. In this paper, we developed a systematic model by taking into account the influence of excitation of neutral alkali atoms to even-higher levels and their ionization on the physical features of a static DPAL. The procedures of heat transfer and laser kinetics were combined together in our theoretical model. By using such a theme, the continuous temperature and number density distribution have been evaluated in the transverse section of a cesium vapor cell. The calculated results indicate that both energy pooling and ionization play important roles during the lasing process. The conclusions might deepen the understanding of the kinetic mechanism of a DPAL.