Regenerative cooling of the high-temperature components in propulsion and power-generation systems plays a paramount role in maintaining the reliability and durability of the systems. In this paper, a mathematical model is developed for studying fluid dynamics and heat-transfer characteristics of the aviation kerosene RP-3 at supercritical pressures. The model accommodates a detailed pyrolytic chemical reaction mechanism, which consists of 18 species and 24 elementary reactions (Jiang, R.; Liu, G.; Zhang, X. Thermal cracking of hydrocarbon aviation fuels in regenerative cooling microchannels. Energy Fuels 2013, 27, 2563-2577). Accurate calculations of thermophysical properties at supercritical pressures are properly incorporated. After rigorous model validations, numerical studies of turbulent heat transfer of RP-3 in a micro cooling tube at a supercritical pressure of 5 MPa are conducted under operating conditions of both constant wall heat flux and constant surface temperature to obtain a fundamental understanding of the complex physicochemical processes. Results indicate that the endothermic fuel pyrolysis, which prevails once the bulk fluid temperature rises above 750 K, dictates the fluid flow and heat-transfer process in the high fluid temperature region. Significant variations of the fluid thermophysical properties also make strong impacts; two scenarios of heat-transfer enhancement resulting from property variations under the tested conditions are analyzed. This work has fundamental and practical implications for effective thermal management in propulsion and power-generation systems.