This study represents the development of a hybrid version of the strong form meshless method that combines Radial Basis Function - Finite Differences (RBF-FD) with a classical finite difference method. This novel hybrid version successfully solves thermo-mechanical problems with discontinuous differentiable material parameters occurring in non-linear path-dependent materials. Local interpolation problems are composed of augmented polyharmonic splines and second-order finite differences. For the Neuman type of boundary conditions, a novel technique of stabilisation is presented. A one-way coupled thermo-mechanical model is introduced where temperature difference governs the mechanical model. The solution procedure is implemented in 2D (plane strain) and 2.5D (generalised plane strain) and verified on thermo-elasto-plastic and visco-plastic benchmarks. A successfully developed method is demonstrated in two high-temperature steel production processes. Firstly, in the solidification of square steel billets in the continuous casting. A 2.5D travelling slice (TS) is considered which travels along the casting direction and enables the introduction of the straightening process. The cooling of the TS and the inner ferrostatic pressure governs the thermo-elasto-visco-plastic mechanical response to predict the critical areas prone to hot-tearing. The developed 2.5D model is subsequently applied to the modelling of cooling of long steel bars on a cooling bed. It considers a set of bars positioned on the cooling bed, that affect each other via radiation and computes the thermo-mechanical response with induced residual stresses and bars bending. The presented study shows the novelty and applicability of a new method to complex industrial steel production processes.