This paper is concerned with a method for calculating the thermal-stress distribution in a plate exhibiting temperature-dependent properties. Using the perturbation method, general equations for the displacements are found. The equations can be solved by using four displacement functions. Following this method, a solution is derived for calculating the stress intensity factor for a Griffith crack in a temperature-sensitive plate under a linear temperature distribution, where we assume that the temperature field is not disturbed by the crack. (Under these conditions, if a plate is temperature-insensitive, the stress intensity factor for the crack is zero.) In this case, whether the stress intensity factor is zero or not depends only on the temperature variation of the coefficient of thermal expansion. A numerical example is given for a plate made of steel.