Abstract: Taking into account non-Darcy flow within fractures and local thermal non-equilibrium (LTNE), an improved thermal-hydraulic-mechanical coupled model is established for CO₂ multi-stage hydraulic fracturing EGS. The study comprehensively analyzes the mechanisms of fluid flow and heat transfer within complex fracture networks. A comparative analysis of the thermal performance of CO₂ multi-stage hydraulic fracturing EGS under varying fracture network configurations is conducted, elucidating the respective roles of primary fractures, secondary fractures, and natural fractures in the heat extraction process. It also investigates the influence of key fracture parameters, such as the number of primary fractures, the aperture of primary fractures, the horizontal length of secondary fractures, and the permeability of natural fractures, on the thermal extraction efficiency of EGS. The results indicate the presence of non-Darcy flow within the fracture network, particularly pronounced in primary fractures. In comparison to cases considering only primary and natural fractures, the inclusion of secondary fractures leads to an 80.36% increase in accumulative energy extraction. Conversely, neglecting both primary and secondary fractures results in a 64.58% reduction in accumulative energy, underscoring the pivotal role of artificial fracture networks in enhancing heat extraction performance. Moreover, the number of primary fractures exerts the most substantial influence on thermal recovery efficiency, with the highest accumulative energy observed when secondary fractures directly intersect. This research provides critical insights for the optimization of EGS in complex fracture networks.