The integral method of calculating thermal and dynamic boundary layers at the end surface is combined with calculating the gas dynamic characteristics of the flow in the vane channel and the end surface temperature state using the finite element method. A field of stream lines and equipotentials is obtained as a result of the gas dynamic calculations. Thus a mesh is formed for solving integral equations obtained for a quasi three-dimensional boundary layer. The solution of these equations makes it possible to determine boundary conditions for calculating the end wall temperature state. The advantage of this calculation procedure is its economy from the point of view of the time required for calculation and the use of the on line memory capacity as compared to the time required for solving the complete system of the equations of motion and energy for the case under consideration.