Accurate heat flux predictions are essential for the development of thermal protection systems for hypersonic re-entry capsules. The Japan Aerospace Exploration Agency (JAXA) has developed a High-Enthalpy Shock Tunnel (HIEST) and conducted heat flux measurements on an Apollo-shaped capsule to investigate aeroheating characteristics under forced turbulent conditions. Reynolds-averaged Navier–Stokes (RANS) simulations have also been performed to validate the experimental results. However, RANS simulations often have difficulty capturing unsteady turbulent features with sufficient spatiotemporal resolution, and accurate prediction of laminar–turbulent transition and aeroheating remains challenging. In this study, large-eddy simulations (LESs) were performed to investigate laminar–turbulent transition and heat flux on an Apollo-shaped capsule. “Pizza-box” roughness elements were installed on the front surface of the capsule to induce a forced laminar–turbulent transition. Hypersonic chemically reacting flows were solved using an OpenFOAM-based solver, with the WALE model employed as the subgrid-scale model. A detached shock wave and a shock layer were formed in front of the capsule, inducing aeroheating on the capsule surface. Vortical structures were visualized using the second invariant of the velocity gradient tensor, confirming the generation of hairpin vortices downstream of the roughness elements. The Stanton number in the forced turbulent state with roughness was approximately 1.6 times larger than that in the laminar state without roughness, showing good agreement with experimental results. The increase in the Stanton number was observed at locations where hairpin vortices were generated. The present LESs successfully revealed the coupled effects of flow structures and aeroheating characteristics of the Apollo-shaped capsule, which are difficult to capture using conventional RANS simulations.