CO2 is being considered as an effective alternative working fluid for geothermal applications due to its superior fluid dynamics and heat transfer properties compared to water. Utilizing sedimentary rocks for geothermal energy recovery through a CO2-plume geothermal system, especially in carbonate reservoirs, has been shown to be a practical approach that eliminates the need for hydraulic fracturing. However, uncertainties remain regarding the thermal and hydraulic behavior, particularly the chemical interactions between CO2 and carbonate rocks. This study develops a comprehensive wellbore–reservoir coupling reactive transport model based on specific information obtained from the Ordovician limestone geothermal reservoir in Shandong, China. The model aims to assess the feasibility of heat extraction in carbonate reservoirs by evaluating the heat extraction performance and fluid–rock interaction. The results indicate a rapid temperature drop after CO2 breakthrough due to the Joule–Thomson effect. Simultaneously, the fluid transitions into and maintains a two-phase state throughout the operation. Chemical reactions within the reservoir are not aggressive since complete mixing between unsaturated water and CO2 only occurs in the vicinity of the production well, highlighting the potential of utilizing carbonate reservoirs for efficient heat extraction in geothermal systems. Further research is needed to optimize the performance of CO2-based geothermal systems in carbonate reservoirs.