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While multi-energy microgrids (MEMGs) offer a promising approach to reduce energy consumption through coordinated integration of various energy vectors, research has primarily focused on static studies. These studies aim to optimize a particular cost function but neglect the dynamic aspects of the system operation. This paper presents a dynamic model of an MEMG comprising of electricity and thermal vectors. A novel dynamic fuzzy logic-based energy management system (EMS) is investigated, aiming to ensure energy balance (electric and thermal), optimize renewable energy utilization, and reduce the reliance on the local electricity grid and gas. Both the EMS and MEMG have been evaluated under different weather conditions and a 4-hour variable load profile. Furthermore, the EMS effectiveness has been verified through a real-time experiment using an OPAL-RT4512 unit and a dSPACE MicroLabBox prototype. The results show that the proposed fuzzy logic-based EMS outperforms a conventional EMS based on machine states (states-based EMS), achieving a notable reduction in electricity grid consumption of 80%, as well as a consumption reduction of 7.4% in the gas boiler and 5.4% in the electric boiler. Furthermore, the control performance results in a remarkable reduction in ITAE (42.57%), ITSE (89.10%), IAE (54.36%) and ISE (57.55%) for the hot water temperature control, and in ITAE (17.06%), ITSE (52.50%), IAE (31.19%) and ISE (29.99%) for the heating control.