In this paper, Kirchhof's transform is employed to convert time dependent heat conduction problems involving varing material properties and mixed and nonlinear radiation boundary condictions into a linear one. Appling weighted residual method to transform the problem in boundary integral equation. Discretization of this equation gives a system of algebraic equations with linear matrix and nonlinear right band sides. Such set of equations can be solved itera-tively. The two dimension linear-nonlinear transient temperature field analysis program is developed, and several numerical examples are computed in the paper.