Analysis of the operation of flowing-gas low power DPALs is crucial for designing high power devices. In particular, the comparison between the measured and calculated temperature rise in the laser cell makes it possible to estimate the contribution of the quenching of the alkali atoms electronic states to the gas heating. Here we report on an experimental and theoretical study of continuous wave flowing-gas Cs DPAL with He and CH4 buffer gases, flow velocities of 1-4 m/s and pump powers of 30-65 W. In the calculations we used a 3D computational fluid dynamics model, solving the fluid mechanics and kinetics equations relevant to the laser operation. Maximum CW output power of 24 W with a slope efficiency of 48% was obtained. The experimental and theoretical values of the power and gas temperature are in good agreement. The lasing power was not affected by the flow velocity at this range of pump power and the gas temperature rise was only several degrees. It was found that the best agreement between the measured and calculated temperature rise is achieved for quenching cross-section ~0.05 Å2.