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This paper presents an economic model predictive control approach for a linear microgrid model. The microgrid in grid-connected mode represents a medium-sized company building including storage systems, renewable energies and couplings between the electrical and heat energy system. Economic model predictive control together with Pareto optimization is applied to find suitable compromises between two competing objectives, i. e. monetary costs and thermal comfort. Using real-world data from 2018 and 2019, the model is simulated with auto-detection of the Pareto solution which is closest to the Utopia point. The results show that the Pareto optimization can either be used in real-time control of the microgrid, or to obtain suitable weights from long term simulations. Both approaches result in significant cost reductions.