Intersubband electron scattering transport in terahertz GaAs-AlGaAs quantum cascade lasers is analyzed, using a full 13-level self-consistent rate equation model. The approach includes all relevant scattering mechanisms between injector-collector and active region states in the cascade structures. Employing an energy balance equation which includes the influence of both electron longitudinal optical phonon and electron-electron scattering, the method also enables evaluation of the average electron temperature of the nonequilibrium carrier distributions in the device. The electron temperature is found to give a strong influence on the output characteristics, particularly at very low temperatures. The threshold currents and electric field-current density characteristics are in very good agreement with experiment, implying that the model has a strong predictive capability.