Nonhomogeneous materials, such as functionally gradient materials (FGM), have special characteristics due to arbitrarily distributed and continuously varied material properties. For such nonhomogeneous materials, the heat conduction equation is presented in a nonlinear form. In this paper, the temperature solution for such a nonlinear system is formulated approximately, and the solution of the integral form of nonuniform thermal material constants is given. Taking into account the effect of temperature dependency of material properties, the one-dimensional transient heat conduction problem of such a nonhomogeneous plate is analyzed theoretically, and the associated thermal stress distribution is formulated under the mechanical of traction-free condition. Numerical calculations are carried out for a nonhomogeneous plate made of Zirconium Oxide and Titanium alloy. The influence of a temperature dependency in material properties and of a change of nonhomogeneity affected by the temperature and the thermal stress distributions are shown in figures and examined briefly in the text.