Functionally graded materials represent an innovative class of composite materials characterized by a spatial variation in structure and composition, resulting in tailored properties suitable for specific applications and operational conditions. Initially developed for thermal barrier applications in space shuttles, these materials have found diverse applications in aerospace, automotive, defense, biomedical, and other fields. While significant research has been conducted on the fracture behavior of functionally graded materials under mechanical loading, there remains a notable gap in understanding crack initiation and propagation under intense thermal loads. This presentation introduces a computational framework designed for the numerical simulation of dynamic crack propagation in functionally graded materials subjected to thermal shocks. The methodology relies on a coupled thermal-mechanical phase field model of brittle fracture, incorporating a temperature-dependent elastic energy density function. The presentation provides a comprehensive overview of the mathematical and implementation aspects of the approach, with verification and validation against alternative computational methods and experimental findings. Furthermore, the proposed framework is applied to challenging thermal shock scenarios, demonstrating its capability to capture the intricate physics governing the coupled thermal-mechanical-fracture behavior of functionally graded materials in extreme environments. The outcomes of this research hold significant importance in predicting and preventing sudden loss of load-carrying capacity and catastrophic failure in applications characterized by severe loading conditions and extreme thermal environments.