This article sets forth two different computational methods developed to evaluate fracture parameters for inclined cracks lying in orthotropic functionally graded materials, that are under the effect of thermal stresses. The first method is based on the J(k)-integral, whereas the second entails the use of the J(1)-integral and the asymptotic displacement fields. The procedures introduced are implemented by means of the finite element method and integrated into a general purpose finite element analysis software. Numerical results are generated for an inclined edge crack in an orthotropic functionally graded layer subjected to steady-state thermal stresses. Comparisons of the mixed-mode stress intensity factors computed by the use of the proposed methods to those calculated by the displacement correlation technique point out that both approaches lead to numerical results of high accuracy. Further results are provided in order to illustrate the influences of inclination angle, material property gradation, and crack length upon the thermal fracture parameters.