Numerical studies on the flow and heat transfer characteristics of rectangular regenerative cooling passages with lateral curvature for a high-area-ratio nozzle are presented. Unlike regular geometries of coolant paths used in various engineering applications, high-area-ratio rocket nozzles have steeply curved surfaces over which the cooling passages are provided. Though the inherent inward curvature benefits heat transfer enhancement in the throat region, it is insufficient to circumvent peak heat dissipation demand. Hence, the heat transfer enhancement due to lateral curvature of the coolant fluid passages provided near the throat region is explored in this study. Extensive numerical simulations have been performed to analyze the effect of the geometry of the cooling channel on its flow and heat transfer characteristics. The compressible turbulent flow field inside the nozzle has been resolved to understand the realistic local wall heat transfer characteristics of the typical high-area-ratio rocket nozzle using Advection Upstream Splitting Method (AUSM) scheme-based finite volume solver. Menter’s Shear Stress Transport k–ω turbulence model is used to model the turbulent flow inside the nozzle. Simulations of the incompressible coolant flow and conjugate heat transfer in regenerative cooling passages have been performed with realistic spatially varying local heat flux profiles, resulting due to compressible gas expansion in the convergent–divergent nozzle. Secondary flow structures are formed due to the lateral curvature of the coolant fluid passages and are found to enhance the heat transfer considerably. Further, the effect of coolant flowrate and channel curvature have been examined to explore its suitability to negotiate the peak heat flux dissipation demand at the throat region of the nozzle.