The application of the Jacobi elliptic functions to heat transfer problems is proposed for the first time by the authors. The applications to a flat plate and a cylinder, which have already been solved, are assured firstly. The authors apply elliptic functions to heat conduction problem combined with thermal radiation and convection, which has not been solved so far. The order of accuracy of numerical calculations are O(h^5). It is shown that the non-linear boundary condition of the second kind is reduced to the linear boundary condition of the first kind which is very simple, by the application of the Jacobi elliptic functions.