This study developed an integrated numerical framework for fluid–solid conjugate heat transfer by unifying the governing equations of fluid dynamics and structural thermal conduction into a single integral formulation. The methodology, validated through a cylindrical leading-edge model, demonstrates high fidelity in capturing the interaction between shock-induced heat flux and structural thermal conduction. The framework was applied to analyze a three-dimensional multilayered thermal protection structure under hypersonic conditions, incorporating radiative heat dissipation at the thermal barrier layer (emissivity = 0.8). Key findings reveal a stark contrast in radiation’s impact: while negligible for the flow field (peak temperature ~1750 K), radiation reduces the structural peak temperature by 26% and homogenizes thermal gradients across complex curved surfaces. Radiation mitigates localized heating at geometric discontinuities by establishing uniform heat dissipation pathways, overriding conduction limitations imposed by irregular geometries. The study advances conjugate heat transfer modeling capabilities, offering insights for optimizing hypersonic vehicle thermal management under extreme aerothermal loads.