In this work, the thermal contact problem of a rigid flat punch sliding over functionally graded material (FGM) coating with a surface crack is investigated. The surface of a homogeneous isotropic substrate is ideally coated by FGM. The coefficient of friction on the contact surface is assumed to be constant, and dry Coulomb friction law is applied. The major purpose of this study is to compute the stress intensity factors at the tip of a surface crack under thermomechanical loading. In this perspective, the thermoelastic contact and the surface crack problems are modeled using finite element method. An iterative solution procedure based on finite elements is developed to solve the contact/crack problem until generated frictional heat reach the steady-state condition. Obtained results are compared to those available in the open literature, and a good agreement is observed. Presented results involve stress intensity factors computed under various thermoelastic sliding conditions.