In our work, we investigate the influence of the post-sintering residual stresses in multi-material ceramic components on the thermal shock resistance. Investigated ceramic composites were made of alumina and zirconia-toughened alumina. This work uses a coupled stress-energy criterion of the finite fracture mechanics to provide insight into the influence of residual stress and sensitivity of critical temperature difference to the tensile strength. Overall, our work contributes to better understanding of the fracture mechanics of multi-material components subjected to strong thermal shock conditions. These findings have significant implications for designing and optimizing damage resistant materials and structures exposed to thermal shock.