Interfacial heat transfer across curved surfaces has not been understood sufficiently well. The present study reports a significant decrease in heat transfer at a convex fluid-solid interface. Effects of curvature on the Kapitza length and the thermal accommodation coefficient are investigated for both gas and liquid phases to understand the occurrence of large temperature jumps. The study also examines the penetration depth of non-equilibrium effects into gas from the convex surface theoretically and reveals the expansion of the Knudsen layer at convex surfaces. Published by AIP Publishing.