Functionally gradient material (FGM) developed for heat-shielding structure is often used
in the very high temperature environment. Therefore, the material property parameters are not only
functions of spatial coordinates but also ones of temperature. The former leads to partial differential
equations with variable coefficients, the latter to nonlinear governing equations. It is usually very
difficult to obtain the analytical solution to such thermal conduction problems of FGMs. If the finite
element method is adopted, it is very inconvenient because material parameter values must be
imputed for each element. Hence, a semi-analytic numerical method, i.e., method of lines (MOLs)
is introduced. The thermal conductivity functions do not need to be discretized and remain
original form in ordinary differential equations. As a numerical example, the nonlinear steady
temperature fields are computed for a rectangular non-homogeneous region with the first, the
second and the third kinds of boundary conditions, where three kinds of functions, i.e. power,
exponential and logarithmic ones are adopted for the thermal conductivity. Results display the
important influence of non-linearity on temperature fields. Moreover, the results given here provide
the better basis for thermal stress analysis of non-homogenous and non-linear materials.