Carbon dioxide (CO2) will reach the storage formation at a temperature lower than that of the reservoir, especially for high flow rates. Thus, thermo-mechanical effects might jeopardize the caprock mechanical stability and cause induced seismicity. We perform thermo-hydro-mechanical simulations of cold (liquid) CO2 injection and analyze the impacts on the rock mechanical stability during a 30 year injection period. Injection of cold CO2 develops a cold region around the injection well that induces a thermal stress reduction in the reservoir due to its contraction. Stress redistribution, which occurs to satisfy stress equilibrium and displacement compatibility, causes the horizontal total stress to increase in the lower portion of the caprock. The thermal stress reduction in the reservoir decreases its stability when injecting a constant mass flow rate through a vertical well in normal faulting stress regimes. Such decrease in stability, if sufficiently large, might cause induced seismicity as well as enhancing reservoir permeability and injectivity. However, the caprock tightens due to the increase in horizontal total stress, improving its stability. After a significant improvement in caprock stability during the first years of injection, stability decreases gradually for longer injection times, but the stress state remains more stable than prior to injection, even for stiff caprocks. By contrast, in a reverse faulting stress regime, both the reservoir and the caprock are less stable during the first years of injection, but stability improves subsequently. On the other hand, injecting cold CO2 at a constant mass flow rate through a horizontal well does not significantly affect the caprock stability for the scenarios considered in this study (in both normal and reverse faulting stress regimes). We show that accounting for the thermal expansion of the grains is very important in low porosity formations to avoid simulating artificial porosity and total stress reductions in the cooled region of the caprock that yield unreal high mobilized friction angles in the lower part of the caprock in normal faulting stress regimes. Overall, injecting cold CO2 should not be feared because of the thermal stresses reduction, though care should be taken to avoid excessive induced seismicity.