This contribution presents a partitioning-based coupling of electromagnetic and thermal reduced-order models for power rails used in hydrogen production plants. Power rails, characterized by their capacity to manage megawatt-class power, generate significant heat due to Joule heating, necessitating the analysis of their electromagnetic and thermal interactions. The proposed method leverages system-level simulations and applies model-order reduction techniques to address the complexity and computational demands of finite-element models. By employing a model order reduction, we generated accurate surrogate models with drastically smaller dimensions, enabling efficient simulations. Furthermore, by segmenting the computational domain into regions with “mostly homogeneous” heat generation rates, the number of reduced-order model inputs was reduced from hundreds of thousands to fewer than 20. The results indicate that this approach significantly lowers development costs and accelerates the design process without compromising accuracy.