Although resistance spot welding (RSW) was invented at the beginning of the last century, the online-monitoring and control of RSW is still a technological challenge and of economic and ecological importance. Process, material and geometry parameters of RSW are stored in the database of the process control system. Prospectively, these accumulated data could serve as the base for data-driven and physics-based models to monitor the spot weld process in real-time. The objective of this paper is to present a finite-difference based parallel solver algorithm to simulate RSW time-efficiently. The Peaceman–Rachford scheme was combined with the Thomas algorithm to compute the electrical–thermal interdependencies of the resistance spot welding process within seconds. Finally, the electric–thermal model is verified by a convergence analysis and parameter study.