A moving quenched soda-lime glass plate with an initial edge crack is modeled, applying the eXtended finite-element method (XFEM) in order to investigate the stress field components and Von Mises stress around the crack. The convective heat with moving boundaries is considered in thermal formulation. The Crank–Nicolson time integration scheme is reformed and adjusted with a view to accurately solving the system of transient heat conduction matrix equations. In order to simulate the whole stages of the problem formulation, MATLAB XFEM (MXFEM) codes are written and employed. The stress distribution contours are plotted in detail and the stress fields around the crack tip are compared quantitatively. The variations of stress intensity factors (SIFs) during crack propagation are obtained through the calculation of the domain form of the interaction integral. In order to verify the procedure and display the ability of the developed formulation, the results are compared with experimental outputs from the literature.