In this paper we present thermo-plasticity model for dealing with localized failure with softening, which is capable of accounting for mechanical loading and heat transfer simultaneously. The main point concerns the localized failure of the structure which results with heterogeneity of stress and strain field for temperature dependent properties. We discuss how to employ structured mesh for such case, and construct the appropriate enhancements of the displacement and temperature fields by using the finite element method with embedded discontinuities (ED-FEM). For clarity, we first consider 1D case, and provide several illustrative numerical simulations. We then provide the corresponding generalization of the proposed model to 2D case and its numerical implementation based upon structured ED-FEM mesh.