Jet impingement is often employed within the leading edge of turbine airfoils to combat the heat loads incurred within this region. This experimental investigation employs a transient liquid crystal technique to obtain detailed Nusselt number distributions on a concave, cylindrical surface that models the leading edge of a turbine airfoil. The effect of hole shape and differing hole inlet and exit conditions are investigated. Two hole shapes are studied: cylindrical and racetrack-shaped holes; for each hole shape, the hydraulic diameter and mass flow rate into the array of jets is conserved. As a result, the jet's Reynolds number varies between the two jet arrays. Reynolds numbers of 13,600, 27,200, and 40,700 are investigated for the cylindrical holes, and Reynolds numbers of 11,500, 23,000, and 34,600 are investigated for the racetrack holes. Three inlet and exit conditions are investigated for each hole shape: a square edged, a partially filleted, and a fully filleted hole. The ratio of the fillet radius to hole hydraulic diameter is set at 0.25 and 0.667 for the partially and fully filleted holes, respectively, while all other geometrical features remain constant. Results show the Nusselt number is directly related to the Reynolds number for both cylindrical and racetrack-shaped holes. The racetrack holes are shown to provide enhanced heat transfer compared to the cylindrical holes. The degree of filleting at the inlet and outlet of the holes affects whether the heat transfer on the leading edge model is further enhanced or degraded.