<p>Thermally induced compressive loads can trigger buckling failures in composite structures. Variable-stiffness laminated composites, featuring spatially varying fiber orientations, exhibit superior buckling resistance compared to straight-fiber composites. However, structural analysis and design optimization of variable-stiffness composite structures are computationally demanding, as high-fidelity models are required to accurately capture their spatially varying fiber characteristics. In this work, we develop an efficient multi-fidelity-assisted optimization framework for thermal buckling design of variable-stiffness composites under manufacturing constraints. Based on Gaussian process regressions, the framework introduces a new multi-fidelity model with an exponent-based adaptive correction scheme. A hybrid optimization strategy is developed by combining genetic algorithms for global exploration and sequential quadratic programming for local refinement. Key manufacturing constraints, including maximum fiber curvature, fiber gaps, and overlaps, are simultaneously enforced. The efficacy of the proposed methodology is demonstrated through reliable optimal solutions obtained for two numerical examples involving different boundary conditions and materials.</p>