It is pointed out that the vibrational temperatures of the symmetric stretch and bending modes of CO 2 being almost equal, are close to the translational temperature (T) of the fast-axial-flow continuous wave CO 2 laser plasma. This allows one to base the analysis of the processes in such plasmas on the three temperature approximation (translational temperature, vibrational temperature of the asymmetric stretch mode of CO 2 (T 3) and vibrational temperature of N 2 (T 4)) leading to a substantial reduction of computer time when compared with the conventional five temperature approximation. Approximations of the three temperature model are supported by the results of our computations and by the available experimental data. When applied to the industrial fast-axial-flow laser, our model predicts a gradual increase in T, T 3 and T 4 along the laser axis, with T reaching about 360 K, T 3 and T 4 reaching about 2500 K, which agrees with experimental observations.