The Cooled Cooling Air (CCA) technology could be effectively used in an advanced gas turbine engine to reduce temperature of the highly compressed air and recover its cooling capacity, using the onboard fuel as coolant. Computational investigations are conducted to analyze heat exchange between the supercritical-pressure aviation kerosene and the compressed high-temperature air in a double-pipe counterflow configuration, intended for the CCA applications. The thermal oxidation reactions and surface coking of kerosene are taken into consideration based on a validated chemical mechanism. Results indicate that the air tube diameter should be determined to obtain not only the improved overall thermal performance on the air side, regarding both heat transfer and pressure drop, but also the properly limited maximum temperature on the fuel side to avoid the strong pyrolysis chemical reactions of kerosene and the resulting fast surface coking process. Although the ribbed and dimpled surface structures are both able to improve the overall thermal performance in the fuel tube and increase the bulk air temperature reduction, they also lead to the increased surface coking rate from the thermal oxidation reactions. The thermal oxidative coking process would gradually increase heat transfer barrier and cause an adverse effect on the long-time and efficient operation of a heat exchanger. Numerical results obtained in this paper should have fundamental and practical importance in CCA applications.