To ensure realistic results when modeling welded joints using the finite element method (FEM), it is essential to appropriately characterize the thermo-mechanical behavior of the elastic-plastic Finite Element (FE) models. This task is complex. Any small differences between the actual welded joints and the welded joints based on FEM can be amplified enormously in the presence of nonlinearities. Due to the intense concentration of heat on a small area to create such joints, the regions near the weld line undergo severe thermal cycles. These generate significant angular distortion due mainly to the residual stresses. This paper proposes a method to determine the parameters that are most appropriate for modeling the Butt joint single V-groove welded joint FE models’ thermo-mechanical behavior that were created by the one-pass Gas Metal Arc Welding (GMAW). The method is based on experimental data, as well as genetic algorithms (GA) with multi-objective functions. As a practical example, the proposed methodology is validated with three different welded joints specimens that are manufactured by different voltages and currents (26 volts and 140 amps, 28 volts and 210 amps, and 35 volts and 260 amps). The electrode orientation, shielding gas flow rate, distance between nozzle and plate, and welding speed were considered to be constant for all of the specimens that were studied, and their values were 80°, 20.0 L/min, 4.0 mm, and 6 mm/s, respectively. The base material was EN 235JR low carbon steel, whereas the weld bead was ER70S-6 for the three specimens that were welded. An agreement between the temperature field and the angular distortion that was obtained by the adjusted FE models and those that were obtained experimentally demonstrates that the proposed methodology may be valid for automatically determining the most appropriate parameters.