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A sliding-pressure additive manufacturing technique with low cost and high accuracy based on Joule heat (SP-JHAM) was developed for the small metal parts. The temperature field and thermal history of the system are important for the experiment analysis. In this research, a thermal-electrical-structural coupling finite element simulation model for three-dimensional SP-JHAM process was established. The temperature field variation law during manufacturing, the temperature distributions inside the wire and substrate, and the shape of isothermal surfaces were analyzed. Results show that the Joule heat is generated between the wire and roller, and the internal temperature of wire rises to 2700 °C within 0.1 s. The position of the maximum temperature is moved with the roller moving. The temperature gradient inside the wire presents the arching shape, and that inside the substrate presents the semi-ellipsoidal shape. The simulated cross-section melting regions are in good agreement with the experimental ones. Thus, the established finite element model can accurately simulate the temperature field of SP-JHAM process, which is of great significance for the guidance of mechanism investigation and actual production.