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Geological Carbon Storage (GCS) in deep saline aquifers is an essential technology for mitigating climate change. The injection of large volumes of CO2, often at temperatures lower than the in-situ reservoir conditions, induces complex coupled Thermo-Hydro-Mechanical (THM) processes that can affect the security of storage. This paper details the construction of a fully coupled 3D numerical model to simulate the injection of cold CO2 into a deep, layered saline aquifer. Using the open-source GEOS simulator, we model the interdependent effects of fluid flow, heat transfer, and geomechanics over a 10-year period, including a 5-year injection phase and a 5-year post-injection phase. The model investigates pressure buildup and thermal stress development effects to assess the geomechanical response of the reservoir and, critically, the integrity of the overlying caprock.