Context-aware recommender systems enhance personalization by incorporating situational information beyond traditional user-item interactions. However, they often face challenges due to sparse and heterogeneous contextual signals. We propose EBC-CARS, an energy-based framework that formulates user-item-context interactions as an energy minimization problem, enabling contextual conditions to reshape the compatibility structure in a principled manner. Building upon this formulation, we introduce ED-EBC-CARS, which integrates Energy Distance as a statistically grounded regularizer to mitigate distributional discrepancies under heterogeneous contextual settings. Experimental evaluations on MovieLens-25M, Amazon Reviews, and Yelp demonstrate consistent improvements over conventional collaborative filtering and representative context-aware baselines in terms of RMSE and Precision@10, indicating the effectiveness of distribution-aware energy modeling for stable and reliable preference estimation.