The present paper is concerned with transient thermal stress in a transversely isotropic infinite solid containing an annular crack subjected to heat absorption and heat exchange on the crack surface. Since it is very difficult to obtain an analytical solution for the temperature field, the finite-difference method with respect to a time variable is introduced. Thermal stress is analyzed by means of the transversely isotropic potential functions method. Numerical calculations of the stress intensity factors in transverse isotropy were carried out for a transversely isotropic graphite. Furthermore, the effects of anisotropies of the material constants on the stress intensity factors are investigated.