<p>Diode pumped alkali vapor amplifiers have a great potential to achieve laser power scaling with high beam quality. A three-dimensional multi-physics model including heat transfer, fluid dynamics, gas dynamics, and wave optics was established to simulate the performance of the diode pumped alkali amplifier. Comparison with experiments proves the model to be more accurate than the classical three-level model with a temperature averaging assumption. Using the three-dimensional multi-physics model, the effect of heat deposition on amplification and beam quality is well described. Additionally, the thermal variations in the vapor cell, the near and far fields of the output laser intensity, and the amplifier performance at lower flow rates are analyzed by the model. This model is of great significance for the performance design and optimization of amplifiers.</p>