Reservoir cooling by water or waste-water injection can significantly alter the reservoir stress. The out- of-zone fracture growth is substantially affected by this poro-thermo-elastic stress changes occurring in heterogeneous rock layers. No previous study, however, systematically investgated the influence of heat conduction and convection on the associated stress alteration and fracture height growth during the long- term water injection in multiple layers. Without understanding this coupled effect, which occurs over a long-term fracture propagation, it is difficult to capture the conditions for the fractures to breach into the bounding shale layers. In this paper, we present that the thermal conduction between the injection sand and bounding shale is crucial in predicting the fracture containment during water injection. We developed a fully coupled compositional reservoir/fracturing simulator that solves poro-thermo-elasticity. We used it to simulate 3- dimensional fracture propagation induced by cold water injection and, at the same time, calculate the stress field influenced by the thermo-poro-elastic effect in heterogeneous reservoir layers. Effective stress in the bounding layer is dynamically updated to capture the poro-thermo-elastic effect and associated fracture height growth. We first validate our model with existing analytical solutions and studied a field case. We identify the effects of fluid properties, rock properties, and injection temperature on stress changes and the fracture containment for the first time.