Thermal effects are an important component in the analysis of geologic carbon storage because the injected CO2 reaches the storage formation at a lower temperature than that of the reservoir rock. The main fear is related to the possibility that the shear slip that may occur within the reservoir due to cooling could propagate into the caprock, which could result in CO2 leakage. We model a baserock-reservoir-caprock system in a normal faulting stress regime using an axisymmetric model in which we inject cold CO2 and use an elasto-plastic constitutive model to simulate inelastic deformation. CO2 forms a cold region around the injection well of a significantly smaller extension than the CO2 plume. Within this cold region, inelastic strain is yielded due to the thermal stress reduction caused by the thermal contraction of the rock. This inelastic strain occurs only within the reservoir and does not propagate into the caprock. Actually, the stability of the lower portion of the caprock improves in the cooled region as a result of a stress redistribution that occurs to satisfy stress equilibrium and displacement compatibility caused by the thermal stress reduction of the reservoir. This stress redistribution tightens the caprock and prevents CO2 leakage. Thus, thermally induced stresses are not likely to generate fracture propagation into the caprock in normal faulting stress regimes.