Abstract: An iterative method for solving two-dimensional compressible boundary layer equations and steady state equations of heat conduction simultaneously is presented, and also a FORTRAN program for calculation of the local convec-tive heat transfer coefficients over air-cooled vane surface by means of this method is provided. The approximate integral method is used for solving boun- dary layer equations end the finite element method is applied to calculating the steady temperature field of the blade.The input of the program consists of geometry of the blade, pressure or velocity distribution of gas flow external to the boundary layer, entrance flow conditions, internal cooling conditions, nodal numbers and coordinates of the elements. The output includes all principal boundary layer parameters, such as heat transfer coefficients and temperature distribution on the surface, and temperature distribution inside the blade. A numerical example has been calculated and the results are favourably compared with the theoretical and experimental data given by other authors.