Cold water injection into a hot, fractured, geothermal reservoir may trigger shear activation of pre-existing fractures that can help to enhance reservoir permeability, but may also result in unwanted seismicity. In this paper, we investigate through numerical modeling of a hypothetical geothermal reservoir how injection-induced cooling may influence the potential for shear activation, paying special attention to the evolution of deviatoric stress under various stress regimes. In each case, we consider either a reservoir with homogeneous hydraulic properties or the presence of a more permeable fracture zone intersecting the injection well. This fracture zone is either oriented in the maximum (S-Hmax) or minimum (S-hmin) horizontal stress direction. Our main finding is that depending on the configuration, injection-induced cooling stresses can favor or prevent shear reactivation of the preexisting fracture, and this effect can vary temporally and spatially.