In order to ensure the long-term safe storage of captured carbon dioxide, carbon sequestration has become a crucial step with the increasing number and scale of carbon capture and storage (CCS) projects worldwide. Due to high-pressure low-temperature injection and CO2 corrosion, wellbores are prone to failures such as tubing and packer leakage, resulting in the loss of integrity in CO2 injection wells. This study was conducted to investigate the temperature and pressure variations in CO2 injection wells under tubing and packer leakage conditions. The OLGA transient multiphase flow modeling method was employed to simulate packer and tubing leakage scenarios during multiphase CO2 injection from the wellhead into the formation, and distributed fiber optic data were used to verify the predictive accuracy of the simulation model. The results show that under packer leakage conditions, the temperature at the packer location decreases significantly with increasing injection rate and duration, exhibiting a pronounced Joule–Thomson effect. The simulation results were found to be in good agreement with the measured distributed fiber optic temperature profiles, confirming the high predictive accuracy of the model. Under tubing leakage conditions, temperature fluctuations are mainly concentrated at the leakage point, and the magnitude of temperature drop increases significantly with injection rate and duration, further confirming the significant influence of the Joule–Thomson effect. At the same time, with increasing wellbore depth, the phase of CO2 transitions through gaseous, liquid, and supercritical states, a process primarily controlled by depth, pressure, and temperature. It is concluded that through simulation, temperature and pressure variations under different tubing failure conditions can be accurately predicted, providing insights into CO2 phase transitions at different depths and phase change characteristics at leakage points. This study provides a theoretical foundation for fault diagnosis and annulus pressure management of CO2 injection wells, thereby contributing to the reduction of safety and environmental risks during CO2 injection operations.