CO2 injection into unconventional gas reservoir has been recognized as a promising approach to enhance unconventional gas recovery (CO2-EUGR) and sequester CO2 geologically. The CO2-EUGR is a complex multi-physics coupling process. To accurately assess the effectiveness of different injection strategies, this paper firstly presents a non-isothermal compositional two-phase flow model coupling with geomechanics, in which a multicomponent adsorption kinetics is incorporated to separate free phase and adsorbed phase. A hybrid numerical approach combining EbFVM and GFEM is used for numerical solutions. The performance of different injection strategies for CO2-EUGR is evaluated. The results indicate that CO2 injection is able to improve CH4 recovery significantly, over 90 % of injected CO2 can be adsorbed in reservoirs, The performance of CO2-EUGR is permeability dependent, the displacement effect occurs earlier when reservoir permeability is higher; Increase in temperature of injected gas and mixed CO2/N2 injection can further improve CH4 recovery, especially for low permeability gas reservoirs; Mixed gas injection also enables displacement effect to occur earlier; Cyclic injection can hardly lead to increase in CH4 production, especially when reservoir permeability is higher, while it can cause an increase in amount of adsorbed CO2 during injection period. Based on these findings, a geothermal-assisted CO2-EUGR method is proposed.