Abstarct: In this thesis, a homogeneous isotropic medium with temperature-dependant material properties containing a crack has been studied under a classical thermal shock. For this purpose, the coupled governing equations for the thermally nonlinear classical theory of thermoelasticity are derived. After nondimensionalizing and writing the weak form of the governing equations, the eXtended finite element method (XFEM) is utilized for their discretization. The Newmark direct iteration method is used for solving the coupled nonlinear thermoelastic equations in the time domain. Finally, the thermal stress intensity factors (SIFs) are extracted using the interaction integral method. First, two numerical examples are given to validate the written code. Then, three more numerical examples are presented to obtain the thermal SIFs and analyze them in cases where boundary conditions and crack geometry are different. The results show that the thermally nonlinear classical theory of thermoelasticity differs slightly from the linear state when the material properties are temperature- independent, but increases when the material properties are temperature-dependent.