Real time simulations of welding processes remain intractable despite the impressive increasing computing power. This paper presents the case of a thermo-elasto-plastic problem with located moving heat loading. A novel non-intrusive a posteriori reduced order strategy for building multiparametric computational vademecum dedicated to real-time simulations of nonlinear thermo-mechanical problems is proposed. The high order proper generalized decomposition (HOPGD) is used to seek separated representation of solutions with some precomputed snapshots. Furthermore, a relaxation method is successfully applied to accelerate this procedure. The accuracy of the constructed computational vademecum is controlled by a localized multigrid selection method that allows an automatic selection of snapshots in the areas of interest of the parameter space. Examples of multiparametric computational vademecum taking into account some material parameters will be shown in this paper.