To enhance the heat-transfer performance of scramjet engines, a numerical simulation was conducted on the heat-transfer process of RP-3 aviation kerosene under supercritical pressure within a horizontal micro-fine circular tube. The intrinsic mechanism of the heat-transfer process was analyzed, summarizing the impacts of mass flux, inlet temperature, and gravitational acceleration. Furthermore, four commonly used buoyancy criterion numbers were compared and evaluated. The results indicate that the heat-transfer process can be divided into five phases: heating inlet phase, normal heat-transfer phase, heat-transfer deterioration phase, heat-transfer enhancement phase, and high-temperature normal heat-transfer phase. The heating inlet phase is significantly influenced by the inlet temperature, while the heat-transfer deterioration is affected both by the thermal property variations of the aviation kerosene and the buoyancy effects. Lower mass flux and hypergravity conditions all exacerbate heat-transfer deterioration. Inlet temperature, however, does not affect the heat-transfer pattern. Among the criteria, Grq/Grth provides the best prediction of buoyancy effects in horizontal circular tubes.