Rising digitization in industrial production sites and processes offers the opportunity to implement optimization approaches for operational strategies of decentralized energy supply systems (DESS). Current model-based approaches like mixed integer linear programming (MILP) often neglect modeling temperature dependencies and thermal inertia in complex thermal grids in production sites. In this paper a modular MILP model is presented in a model predictive control (MPC) approach which integrates temperature dependencies and thermal inertia in complex DESS. The validation by simulation shows that the approach manages to map thermal dependencies successfully and reduce energy consumption and cost of the DESS by optimizing temperature levels. Hence the approach enables a stable optimized control of complex DESS.