The present study investigated temperature and thermal stress distributions in a film cooling system with normal injection cooling flow. 3D-numerical simulations using the FEM commercial code ANSYS were conducted to calculate distributions of temperature and thermal stresses. In the simulations, the surface boundary conditions used the surface heat transfer coefficients and adiabatic wall temperature which were converted from the Sherwood numbers and impermeable wall effectiveness obtained from previous mass transfer experiments. As a result, the temperature gradients, in contrast to the adiabatic wall temperature, were generated by conduction between the hot and cold regions in the film cooling system. The gradient magnitudes were about 10~20K in the y-axis (spanwise) direction and about 50~60K in the x-axis (streamwise) direction. The high thermal stresses resulting from this temperature distribution appeared in the side regions of holes. These locations were similar to those of thermal cracks in actual gas turbines. Thus, this thermal analysis can apply to a thermal design of film cooling holes to prevent or reduce thermal stresses.