Abstract: Radiology AI systems increasingly inform clinical decisions such as triage, follow-up imaging, and treatment planning. For these decisions to be made safely, model outputs must be well calibrated, meaning predicted probabilities accurately reflect true risk. Many standard techniques for improving calibration, such as MC Dropout and Deep Ensembles, require access to model parameters or retraining. However, proprietary clinical AI systems operate as black boxes, preventing access to the model's internals. To that end, we propose a model-agnostic framework for improving calibration of black-box models using clinically grounded test-time augmentation (TTA). Our framework applies geometric and physics-inspired 3D CT perturbations and learns probability-level aggregation strategies without access to model internals or the original training data. Across pulmonary embolism and intracranial hemorrhage detection tasks, DualTTA achieved the strongest overall calibration among TTA methods, reducing the Expected Calibration Error by 54% (0.239 -> 0.109) and 43% (0.051 -> 0.029), respectively, while requiring only input-output access. Additionally, DualTTA outperformed uncertainty estimation techniques that require access to model internals, such as Temperature Scaling, MC Dropout, and Deep Ensembles, in most calibration metrics. These results demonstrate that learned TTA aggregation can improve the calibration of clinical AI systems, providing a practical approach for improving the reliability of black-box medical AI.