The downhole coaxial heat exchanger (DCHE) is expected to exploit medium-deep geothermal resources because of its large heat transfer area. For this geothermal system, the working fluid is injected from the annulus and produced from the central insulated tubing. There have been many studies on the heat extraction performance of DCHE. However, to the best of our knowledge, most previous heat transfer models did not consider the fluid flow in the reservoir, which has a significant effect on DCHE performance. Thus, an unsteady-state heat transfer model considering heat conduction and heat convection of reservoir is presented. The finite difference method is employed to solve the mathematical model. The temperature distribution in the wellbore and nearby reservoir during the exploitation process are analyzed. Subsequently, the effects of the key factors, including flow velocity in reservoir, aquifer thickness, and thermal conductivity of cement on the heat extraction performance are studied. The simulation results depict that the temperature decreases sharply near the wellbore. The temperature impact scope in the reservoir without geothermal fluid is about 20 m, while it reaches 40 m in the aquifer. This indicates that the fluid flow in the reservoir can enhance the heat transfer of DCHE and improve the heat extraction performance. The increase of flow velocity in reservoir will increase the outlet temperature and thermal power. As the aquifer thickness increases, the outlet temperature and thermal power increase. Besides, the outlet temperature and thermal power have a remarkable decrease at the initial stage, but then remains relatively stable. The findings can offer guidance for optimal design of DCHE geothermal system.