Multi-energy microgrids (MEMGs) have emerged as an effective solution for reducing greenhouse gas emissions. These systems leverage the coordination of multiple energy vectors to enhance efficiency and achieve greater independence from the main grid. This paper introduces a dynamic fuzzy-logic energy management system (EMS) designed for a MEMG that encompasses gas and electricity energy vectors. The thermal network of the MEMG comprises a gas boiler, an electric boiler, and a heat load. In parallel, the electrical network consists of a photovoltaic (PV) system, a battery energy storage system, an electric load, and a connection with the grid. The EMS plays a crucial role in evaluating the PV power generation and electric demand, and it adjusts the water temperature in the electric boiler to minimize reliance on the local grid. To evaluate the effectiveness of the MEMG and EMS, a simulation spanning 4.5 hours was conducted under various operating conditions for sun irradiance, heat, water, and electric demand. The results demonstrate the capability of the fuzzy-logic based EMS to reduce the dependence on the local grid, thereby showcasing the suitability of this approach in MEMGs.