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The technology used to enhance coalbed methane (CBM) recovery by injecting CO₂ (CO₂-ECBM) with heat, combining heat injection with CO₂ injection, is still in its infancy; therefore, theoretical studies of this CO₂- ECBM technology should be perused. First, the coupling equations of the diffusion–adsorption–seepage–heat transfer fields of gas are established. The displacement processes under different pressures and temperatures are simulated by COMSOL. Finally, the displacement effects, a comparison of the CO₂ storage capacity with the CH₄ output and the effective influencing radius of CO₂ injection are analyzed and discussed. The results show that (1) the displacement pressure and temperature are two key factors influencing the CH₄ output and the CO₂ storage capacity, and the increase in the CO₂ storage capacity is more sensitive to temperature and pressure than the CH₄ output. (2) The gas flow direction is from the injection hole to the discharge hole during the displacement process, and the regions with high velocity are concentrated at the injection hole and the discharge hole. (3) A reduction in the CH₄ concentration and an increase in the CO₂ concentration are obvious during the displacement process. (4) The effective influencing radius of injecting CO₂ with heat increases with the increase in time and pressure. The relationship between the effective influencing radius and the injection time of CO₂ has a power exponential function, and there is a linear relationship between the functional coefficient and the injection pressure of CO₂. This numerical simulation study on enhancing CBM recovery by injecting CO₂ with heat can further promote the implementation of CO₂- ECBM project in deep coal seams.