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Matrix acidizing is widely used to enhance oil/gas production in the exploitation of carbonate reservoirs. In this work, a three‐dimensional (3D) hydro‐chemical‐thermal (H‐C‐T)‐coupled model was presented to improve the understanding of the acidizing process. The influence of different influencing factors was analyzed, especially the coupling effect of natural fractures and in situ stress. With the increase in acid injection concentration, the minimum pore volume of acid required for breakthrough (PVBT) decreases. The optimal injection rate and the minimum PVBT increase with increasing initial reservoir temperature. With the increasing initial reservoir permeability, the minimum PVBT increases. With the increasing initial reservoir pore diameter and specific surface area, the minimum PVBT and the optimal acid injection rate increase. When the fracture direction is perpendicular to the direction of the maximum principal stress, the fracture apertures decrease with the increase of the maximum principal stress, which leads to an increase in PVBT and wider paths of wormholes. Lastly, the present H‐C‐T‐coupled model was applied in the context of Tahe reservoir exploitation, which shows that optimizing the acid injection rate is able to enhance the connection between wellbores and natural caves.