The utilization of decentralized micro gas turbine combined heat and power (MGT-CHP) units is considered as a prospective technique in power generation due to its high levels of fuel utilization rates and low emissions. However, the inherent strong coupling and complex timescale multiplicity make it challenging to realize optimal operation. To this end, this paper first establishes a precise mechanism model to attain a thorough understanding of the system properties. By conducting singular perturbation theory, the complex nonlinear system is decomposed into a fast power subsystem and a slow heat subsystem. Then, a dual-time-scale zone economic model predictive control (D-ZEMPC) algorithm, which is comprised of a fast EMPC and a slow EMPC, is applied to achieve dynamic synergy between heat and power supply by actively coordinating the two sub-controllers. Moreover, a zone tracking method is introduced for room temperature control, thereby yielding increased freedom in balancing the economic profits and thermal comfort. The simulation results in three scenarios along with the qualitive and quantitative discussions show that compared with the other two centralized EMPC algorithms, the proposed D-ZEMPC can significantly alleviate computational loads and reduce the simulation time by over 64.5% while maintaining required thermal comfort with minimum fuel consumption.