Advances in aero engine technology have reduced jet and fan noise, which has increased the significance of combustion noise and the need to reduce the indirect noise generated by entropy fluctuations as they accelerate through the turbine stages. The present work examines the influence of film cooling on the convection and attenuation of entropy wave as well as the indirect entropy noise generated in a two dimensional stator cascade using an unsteady RANS modelling approach. Initially the mean flow properties of the stator are compared with experimental data from the Politecnico di Milano for an axial turbine stage without film cooling. Afterwards a single film cooling hole is added to the suction side and the pressure side of the stator blade. Results show that the amplitude of the entropy wave reduces due to the secondary flow from the cooling holes. However, the amplitude of the pressure perturbation due to the accelerated entropy wave increases. Both the attenuation of the entropy wave and increasing the amplitude of the generated pressure waves depend on the mass flow rate of the coolant flow.