In this study we consider an inverse problem of linear heat equation with nonlinear boundary condition. We identify the temperature and the unknown radiation term from an overspecified condition on the boundary. At the beginning of the study, Taylor’s series expansion is employed to linearize nonlinear term and then finite-difference method is used to discretize the problem domain. The least-squares method is adopted to modify the solution. To regularize the resultant ill-conditioned linear system of equations, we apply the Tikhonov regularization method to obtain the stable numerical approximation to the solution. Results show that an excellent estimation can be obtained within a couple of minutes CPU time at pentium IV-2.4 GHz PC.