Previous studies have shown that leak electrons in cusped field thrusters can move along the channel axis to the anode after crossing the magnetic cusp on the exit. In this paper, a one-dimensional fluid model is built along two typical electron paths to study the influence of leak electrons on the discharge characteristics of a cusped field thruster, considering the electron temperature equation. It is found that the frequencies of low-frequency oscillations increase with a decrease in the proportion of leak electrons, which is related to an increase in the ion speed in the channel. Simulation results show that the position of the peak electron temperature is near the magnetic cusp on the exit and the position of the peak electron density is located downstream from the middle magnetic tip. With a decrease in the proportion of the leak electrons, the peak electron temperature and peak electron density decrease and the position of the peak electron density moves away from the exit, which is related to a decrease in the potential fall on the exit and an increase in confinement of electrons to the middle magnetic cusp.