An automated procedure is presented for the conjugate, Navier-Stokes/heat- conduction design and analysis of film-cooled turbine airfoil sections. In this procedure, the internal cooling plenums inside of the airfoil and the layer of thermal barrier coating are automatically constructed and computational grids for the main flow-path, cooling plenums, turbine walls, thermal barrier coating, and cooling tubes are generated. Embedded, overlaid grids are used for the cooling tubes allowing for any arbitrary placement without re-gridding of the main flow-path, turbine walls, or cooling plenums. The multi-disciplinary use of embedded, overlaid-grids makes this approach unique and effective for automated optimization procedures. The techniques used to construct the geometry and various computational grids as well as the treatment of embedded, overlaid grids in the Navier-Stokes procedure are described. Demonstration of the procedure is provided for a transonic turbine vane.