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We employ a Monte Carlo method to investigate the carrier dynamics in the terahertz quantum cascade lasers with vertical and diagonal radiative transition designs. Electron-electron and electron-phonon scattering are included in the calculations and their effects on the temperature dependence of electron transport are evaluated. The simulation shows that the degradation of temperature performance is mainly due to the rapid electron relaxation from upper to lower laser levels, in which the electron-phonon interaction is the dominant scattering mechanism. The parasitic coupling between laser levels is weakened in the diagonal design, resulting in better device performance such as lower current density, higher operating temperature, and less hot electron effects. The calculations are in good agreement with experimental results.