For the cracked plate under transient temperature distribution, J-integral is expressed in the form of line integral by using convolution integral. The J$_{1}$ integral is calculated for a through line center cracked steel plate under thermal and mechanical loading conditions and the calculated values are in good agreement with previous results. The effect of inertia term on the J$_{1}$ integral is not negligible for a glass but for a steel. For the glass plate, the rates of J$_{1}$ integral value to time increase if the values of material properties such as specific heat, thermal conductivity, thermal diffusivity and Young`s modulus as well as crack length and temperature difference in cracked edge increase.