The coupled heat transfer of supercritical-pressure $n$-decane in a concave heated, 90 deg bend, square channel was investigated numerically. Both the geometry and boundary conditions were close to those expected in active-cooled scramjet engines. The effect of secondary motions and wall thermal conductivity on heat transfer was studied. The flowfields obtained by the Spalart–Allmaras model and Reynolds stress model were compared. The secondary flow of Prandtl’s first kind caused by the crosswise pressure gradient in the curved section was 1.0% of the maximum axial velocity. The secondary flow of Prandtl’s second kind caused by Reynolds stress was one magnitude less than that of Prandtl’s first kind. The Spalart–Allmaras turbulence model produced reasonable results with less computational effort than the Reynolds stress model. Secondary flow improves heat transfer by enhancing the mixing of the fluid. Furthermore, higher wall thermal conductivity produces more uniformly distributed temperature and heat flux.