Electron transport in a terahertz GaAs/AlGaAs quantum-cascade laser is calculated using a fully self-consistent intersubband scattering model. Subband populations, carrier transition rates, and current densities are calculated and all relevant intra- and interperiod electron–electron and electron–LO-phonon scattering mechanisms are included. Employing an energy balance equation that includes the influence of both electron–LO-phonon and electron–electron scattering, the method also enables evaluation of the average electron temperature of the nonequilibrium carrier distributions in the device. In particular, the influence of the lattice temperature on the degradation of population inversion and device performance is investigated. The threshold currents, electric-field-current-density characteristics, and temperature-dependent performance are in good qualitative and quantitative agreement with measurement in a recent experimental realization [Köhler et al., Nature (London) 417, 156 (2002)]. Calculations indicate that an important mechanism limiting its operating temperature is the increase of leakage current from the injector to low levels in the active region, and this feature should be improved in future designs.