Increasing performance demands and constraints are necessitating the design of highly complex, integrated systems across multiple sectors, including transportation and energy. However, conventional design approaches for such systems are largely siloed and focused on steady-state operation. To accommodate tightening operating envelopes, new design paradigms are needed that explicitly consider system-component interactions and their implications on transient performance at the system design stage. In this work, we present a model fidelity-based decomposition (MFBD) hierarchical control co-design (HCCD) algorithm designed to optimize system performance characteristics with an emphasis on robustness to transient disturbances during real-time operation. Our framework integrates system level control co-design (CCD) with high-fidelity component design optimization in a computationally-efficient manner for classes of highly-coupled systems in which the coupling between subproblems cannot be fully captured using existing analytical relationships. Our algorithm permits scalable decomposition of computationally-intensive component models and addresses coupling issues between subproblems in part by introducing an intermediate optimization procedure to solve for reduced-order model parameters that maximize the accuracy of the lumped-parameter control model required in the CCD algorithm. We demonstrate the merits of the MFBD HCCD algorithm, in comparison to an all-at-once (AAO) CCD approach, through a case study on aircraft dynamic thermal management. Our results show that our decomposition-based solution matches the AAO optimal cost to within 2.5% with a 54% reduction in computation time.