From literature and our own studies, it is known that the effects of hot gas cross-flow and, in particular, the turbulence of the hot gas flow highly influence the spreading of the coolant in the near hole vicinity. Moreover, the velocity of the hot gas flow expressed by a hot gas Mach number obviously plays a much more important role in the case of diffuser holes than with simple cylindrical holes. To realize a certain blowing rate, a higher pressure ratio needs to be established in the case of higher Mach numbers. This in turn may strongly affect the diffusion process in the expanded portion of a fan-shaped cooling hole. The said effects will be discussed in great detail. The effects of free-stream Mach number and free-stream turbulence, including turbulence intensity, integral length scale, and periodic unsteady wake flow will be considered. The comparative study is performed by means of discharge coefficients and by local and laterally averaged adiabatic film cooling effectiveness and heat transfer coefficients. Both cooling holes have a length-to-diameter ratio of 6 and an inclination angle of 30 deg. The fan-shaped hole has an expansion angle of 14 deg. The effect of the coolant cross-flow at the hole entrance is not considered in this study, i.e., plenum conditions exist at the hole entrance.