Residual stresses can affect both the static strength and the fatigue endurance of welded joints. Residual stresses can be assessed by numerical simulation; however, the simulation of the welding process is a complex task that requires knowledge of several parameters, many of which can only be estimated with some uncertainty. The reduction in the number of these parameters can lead to a more feasible and efficient study. In this work, the finite element method is used to assess the capability of different thermal methods used to simulate a single pass of the gas metal arc welding process in reproducing the temperature distribution around the weld. Results of the simulations are compared to experimental measurements of the surface temperature close to the welding area. The thermal techniques analyzed adopt different levels of complexity, from the basic implementation of a constant initial temperature assigned to a given material volume, to the more comprehensive and widespread Goldak’s double-ellipsoid model. The study shows that, close to the weld seam, very similar thermal behaviors can be achieved by employing each one of the analyzed methods. Secondly, considering the constant initial temperature method, the comparison between experimental measurements and numerical simulations showed a fairly good agreement, suggesting that a relatively simple method (i.e., requiring the setting of only one parameter) can be used to efficiently reproduce the thermal history of a welding process.