Deep shale gas reservoirs have geological characteristics of high temperature, high pressure, high stress, and inferior ability to pass through fluids. The multi-stage fractured horizontal well is the key to exploiting the deep shale gas reservoir. However, during the production process, the effectiveness of the hydraulic fracture network decreases with the closure of fractures, which accelerates the decline of shale gas production. In this paper, we addressed the problems of unclear fracture closure mechanisms and low accuracy of shale gas production prediction during deep shale gas production. Then we established the fluid–solid–heat coupled model coupling the deformation and fluid flow among the fracture surface, proppant and the shale matrix. When the fluid–solid–heat coupled model was applied to the fracture network, it was well solved by our numerical method named discontinuous discrete fracture method. Compared with the conventional discrete fracture method, the discontinuous discrete fracture method can describe the three-dimensional morphology of the fracture while considering the effect of the change of fracture surface permeation coefficient on the coupled fracture–matrix flow and describing the displacement discontinuity across the fracture. Numerical simulations revealed that the degree of fracture closure increases as the production time proceeds, and the degree of closure of the secondary fractures is higher than that of the primary fractures. Shale creep and proppant embedment both increase the degree of fracture closure. The reduction in fracture surface permeability due to proppant embedment reduces the rate of fluid transfer between matrix and fracture, which has often been overlooked in the past. However, it significantly impacts shale gas production, with calculations showing a 24.7% cumulative three-year yield reduction. This study is helpful to understand the mechanism of hydraulic fracture closure. Therefore, it provides the theoretical guidance for maintaining the long-term effectiveness of hydraulic fractures.