In this study, free convective boundary-layer heat transfer with the influence of thermal radiation over a vertical wavy surface is numerically investigated. A suitable coordinate transformation is applied to map the governing equations of the wavy surface onto an equivalent flat surface, thereby simplifying the mathematical formulation. The transformed, coupled nonlinear partial differential equations are solved using an efficient cubic spline numerical method. The effects of key dimensionless parameters, including the radiation parameter, surface heating parameter, Prandtl number, and wave amplitude, on the flow and thermal characteristics are systematically examined. Variations in the local and average Nusselt numbers as well as the skin friction coefficient are presented and discussed in detail. The numerical results reveal that increasing the radiation parameter significantly enhances the overall heat transfer rate. Moreover, it is observed that higher surface heating intensifies both velocity and temperature fields within the boundary layer, leading to an increase in the local and average Nusselt numbers. The findings provide useful physical insight into the combined effects of surface waviness and thermal radiation on natural convection heat transfer, which can be beneficial in the design of thermal systems involving complex surface geometries.