This study reports on heat transfer characteristics on a curved surface subject to an inclined circular impinging jet whose impinging angle varies from a normal position θ = 0 deg to θ = 45 deg at a fixed jet Reynolds number of Rej = 20,000. Three curved surfaces having a diameter ratio (D/Dj) of 5.0, 10.0, and infinity (i.e., a flat plate) were selected, each positioned systematically inside and outside the potential core of jet flow where Dj is the circular jet diameter. Present results clarify similar and dissimilar local heat transfer characteristics on a target surface due to the convexity. The role of the potential core is identified to cause the transitional response of the stagnation heat transfer to the inclination of the circular jet. The inclination and convexity are demonstrated to thicken the boundary layer, reducing the local heat transfer (second peaks) as opposed to the enhanced local heat transfer on a flat plate resulting from the increased local Reynolds number.