The carrier transition rates and subband populations for a GaAs/AlGaAs quantum cascade laser operating in the mid-infrared frequency range are calculated by solving the rate equations describing the electron densities in each subband self-consistently. These calculations are repeated for a range of temperatures from 20 to 300 K. The lifetime of the upper laser level found by this self-consistent method is then used to calculate the gain for this range of temperatures. At a temperature of 77 K, the gain of the laser is found to be 34 cm-1/(kA/cm-2), when only electron-longitudinal-optical phonon transitions are considered in the calculation. The calculated gain decreases to 19.6 cm-1(kA/cm-2) when electron-electron transition rates are included, thus showing their importance in physical models of these devices. Further analysis shows that thermionic emission could be occurring in real devices.