Wellbore integrity is a critical component of long-term carbon storage. Depleted reservoirs that are potential CO2 storage sites, typically contain several wells. Due to years of operations and abandonment, these wells can have cracks in the cement, cement-casing interface, and/or cement-formation interface. During CO2 injection, changes in temperature may result in stress variations that can further damage the well, threatening its integrity. The temperature difference between the cold injected CO2 and warm reservoir, and different thermal properties for the wellbore casing, cement, and the lithology, will stress the near wellbore environment, potentially extending pre-existing defects creating leakage pathways from the storage reservoir to the overlying strata. We have conducted a systematic numerical study to explore the role of CO2 injection temperature, downhole effective insitu horizontal stress, and the thermo-mechanical properties by coupling a linear elastic stress model with heat conduction. We consider conditions in non-perforated casing above the injection zone where conductive heating is dominant. The injection temperatures considered covers current industrial practice as well as sub-zero temperatures. The latter represents direct injection following ship transport, without pre-heating. In this study, we consider the connection between damage risk and the temperature difference between the injected CO2 and the formation and downhole effective in-situ horizontal stress. The study found that the negative impacts of thermal stress in the wellbore environment are mitigated by the presence of effective in-situ horizontal stresses. Stresses normal to the well have the potential to reduce the tensile stress and stress intensity factor. In the absence of sufficient effective in-situ horizontal stress, thermal stress may cause the fracture to propagate due to high stress concentration near the fracture edges. In general, formations with large effective insitu horizontal stress can prevent leakage paths from growing even when large temperature difference exists between the formation and the injected CO2. Our simulations suggest that CO2 can be injected at sub-zero temperatures, suitable for ship transport, when the downhole effective in-situ horizontal stress is greater than 10 or 12 MPa, depending on the location of the pre-existing cracks. For onshore transportation, injection of liquid CO2 results in minimal damage, provided there is ample in-situ horizontal stress.