Optimizing the aerothermal performance of the combustor–turbine interface is an important factor in enhancing the efficiency of heavy-duty gas turbines. Also, it is a key requirement to fulfill the lifetime in this hottest area of the gas turbine. Typically transition pieces of can combustors induce a highly nonuniform swirling flow at the turbine inlet. In order to better understand the impact of the nonuniform combustor flow at the first stage vanes, a combined experimental and numerical study was carried out. The experimental facility consisted of a high-speed linear cascade with four vane passages, including an upstream transition piece, which was representative of a heavy-duty gas turbine can combustor–turbine interface geometry. The experiments were conducted at engine representative Mach numbers, and film cooling effectiveness measurements were performed at three different blowing ratios. Computational fluid dynamics (CFD) Reynolds-averaged Navier–Stokes simulations were undertaken using a commercial flow solver. The numerical model was first validated with the experimental data, using inlet traverse five-hole probe measurements, pressure taps along the airfoil perimeter, and oil flow visualization results. The investigation shows that the position of the vane relative to the combustor transition piece has a significant impact on the vane aerodynamics and also film cooling behavior. This understanding was important for a robust first vane aerothermal design of the GT36.