A new computational method based on the J(k)-integral is developed in order to calculate crack tip parameters for functionally graded materials (FGMs) that are subjected to mixed-mode thermal loading. By using the constitutive relations of plane thermoelasticity, J(k)-integral is modified and reduced to a domain independent form that contains area and line integrals. Temperature fields in FGMs and the components of the J(k)-integral are computed by means of the finite element method. In both thermal and mechanical analyses, finite element models are created utilizing special graded isoparametric elements that possess cubic interpolation. Numerical results are generated by considering an embedded crack under steady-state thermal stresses and periodic interface cracks subjected to thermal shock heating. The J(k)-integral approach is validated and domain independence is demonstrated by providing comparisons of the mixed-mode stress intensity factors to those calculated using an enriched finite element technique. Presented results illustrate the influences of material property gradation and crack geometry on the modes I and II stress intensity factors, energy release rate and the T-stress.