Understanding of convection heat transfer characteristics of fractures is of great significance to improve the heat extraction efficiency of carbonate reservoir. Previous studies on convection heat transfer of fluid flowing through rock fractures are on either granite or sandstone. Limited experimental research has been performed on carbonate fractures after acidizing etching. In this work, an improved test method is developed to analyze the convection heat transfer characteristics of carbonate fractures after acidizing etching under real-time high temperature and high confining pressure. In this method, the traditional test method of convection heat transfer coefficient is improved by monitoring the temperature of inner fracture surface and flowing water. Two thermocouples are especially arranged inside the sample to monitor the temperature of inner fracture surface along the flow direction, and two other thermocouples for the inlet and outlet water temperatures. The results show that the temperature differences between the fracture surface and the flowing water are significantly dependent on confining pressure, fracture roughness and flow rate, and the maximum temperature difference could be reached 2.2 ${}^{\circ }$C, which leads to a significant difference in the convection heat transfer coefficient between the traditional and improved test methods. A larger number of pores, caves, and micro-fractures caused by acid etching are observed on the fracture surface by scanning electron microscopy. The special fracture morphology of carbonate is totally different from those of granite and sandstone in previous studies, and can increase the convection channel and increase the contact area with flowing fluid and results in the inapplicability of the hypothesis to carbonate fractures after acidizing etching. The present work could improve the knowledge of convection heat transfer characteristics of carbonate fractures.