The thermoelastic problem of a heat flux over a region with a crack near a rigid inclusion is studied. The inclusion is assumed fixed, which implies the translation and the rotation are restrained. The crack faces are assumed free of stress. Both of the inclusion and the crack are under thermal adiabatic condition. In the analysis, the original problem was reduced to a series of displacement boundary value problems by using the principle of superposition. The Green’s function method is used to obtain the solution of the prescribed problem in the forms of integral equations. The basic problems therefore become those for an edge dislocation, and for a heat source couple, as well as the problem of a plane containing the inclusion under a uniform heat flux. These problems are solved using the complex variable method along with the rational mapping function technique. The variations of the stress intensity factors at the crack tips with various crack lengths and heat flux angles are shown. The effects of the inclusion shape and size are also investigated.