After second world war, we have seen a very rapid development of Thermoelasticity stimulated by various engineering sciences. As we know, structures behave in different fashion under climate variation and the most responsible factor for these variations is heat which falls through and causes deformation of the body. A considerable progress in the field of aircraft and machine structures, mainly with gas and steam turbine and the emergence of new topics in chemical and nuclear engineering, have given rise to numerous problems in which thermal stresses play an important and frequently even a primary role. The concern of the present paper is the problem of an interior Griffith crack opened by heated wedge in a strip whose edges are normal to crack axis and the medium is assumed to be homogenous and isotropic. Under plane strain condition the closed form expressions for the stress intensity factors and the crack shape are obtained by use of Fourier transform technique. Two special cases of heat distributions are discussed in the end when wedge geometry is prescribed.