This study investigates the aerothermal shape optimization of a two-dimensional baseline geometry, targeting the simultaneous minimization of aerodynamic drag and thermal loads. Optimization is performed over a representative flight trajectory in which operating conditions vary across mission segments. This trajectory-based, multi-objective formulation demands that the geometry maintain robust performance throughout the entire flight profile [1, 2]. A surrogate-based framework is employed in which Gaussian process (GP) models approximate drag and thermal responses using a limited set of high-fidelity simulations. The GP surrogates are built with covariance structures drawn from the standard GP literature [3] and accelerated through GPU-enabled inference techniques [4]. The aerodynamic behavior is simulated using compressible Reynolds-Averaged Navier–Stokes (RANS) equations, while aerodynamic heating analyses are performed in a loosely coupled manner maintaining predictive accuracy at a fraction of the computational cost of tightly coupled analyses [5]. Figure 1 illustrates representative wall-temperature contours for a 15° Cone-Cylinder-Flare (CCF) missile at different trajectory instants, demonstrating the close agreement between the loosely coupled and tightly coupled aerothermal solutions. Design decisions are steered by a multi-objective Expected Hypervolume Improvement acquisition function, which iteratively refines the surrogate models and probes promising regions of the design space [6]. The procedure efficiently uncovers a Pareto front of geometries that offer balanced trade-offs between reduced drag and mitigated thermal loads. Providing this set of Pareto-optimal designs equips decision-makers with explicit alternatives, enabling them to select the solution that best aligns with mission-specific priorities and operational constraints. By operating over a trajectory with varying flight conditions, the proposed methodology demonstrates the robustness, efficiency, and scalability of surrogate-assisted aerothermal shape optimization in realistic mission scenarios. This extension from single-point to trajectory dependent aerothermal problems thereby advances the state of the art in aerothermal shape optimization.