This paper presents the theoretical methodology, conceptual demonstration, and validation of a fully automated computer program for the inverse design and optimization of internal convectively cooled three-dimensional axial gas turbine blades. A parametric computer model of the three-dimensional internal cooling network was developed, including the automatic generation of computational grids. A boundary element computer program was written to solve the steady-state non-linear heat conduction equation inside the internally cooled and thermal barrier-coated turbine blade. A finite element algorithm was written to model an arbitrary network of internal coolant passages for the calculation of the internal heat transfer coefficients, pressure losses, local flow rates, the effects of centrifugal pumping, heating of the coolant fluid, and forced convection from the thermal model of the solid to the coolant fluid. The heat conduction and internal flow analyses were iteratively coupled to account for the heat balance between the blade and the coolant fluid. The computer-automated design and optimization system was demonstrated on the second high-pressure turbine blade row of the Pratt & Whitney F100 engine. The internal cooling configuration and local heat transfer enhancements (boundary layer trip strips and pin fins) inside the three-dimensional blade were optimized for maximum cooling effectiveness and durability against corrosion and thermo-mechanical fatigue.