Vehicle exhaust systems operate in a thermally severe environment where high exhaust-gas temperatures, compact underbody packaging, radiative exposure, and limited local cooling can combine to create fire-prone conditions. The greatest risk is concentrated in the exhaust manifold, close-coupled catalyst, and front-pipe region, where hot external surfaces can overheat nearby polymers, wiring, underbody coatings, leaked fluids, and combustible roadside material. This study presents a design-oriented numerical framework for reducing fire hazard risk through coordinated thermal management of the exhaust system. The framework integrates a one-dimensional gas-to-wall energy model, external convection-radiation analysis, view-factor-based assessment of adjacent panel heating, and a normalized fire-hazard index for screening design alternatives. A representative mid-size passenger-vehicle architecture was evaluated under a high-load baseline condition and an optimized condition combining a low-emissivity heat shield, thin insulation, airflow redirection, and improved stand-off distance from vulnerable underbody regions. For the modeled case, the peak exposed surface temperature in the manifold region decreased from 437.3 C to 390.6 C, while the peak adjacent underbody temperature above the same region decreased from 132.9 C to 61.9 C. The front-pipe adjacent temperature fell from 85.9 C to 51.8 C, and the weighted fire-hazard index decreased by 40.2% relative to the baseline. The results indicate that the most effective strategy is not uniform cooling of the entire exhaust line, but targeted reduction of radiative exposure and locally improved heat rejection around thermally dominant zones. The proposed framework provides a practical basis for early-stage decisions on exhaust routing, shielding, clearance, and material selection.