Due to significant temperature differences between the injected medium and in situ formation, injection of CO₂ (as with water or other cold fluids) at depth induces thermal changes that must be accounted for a complete understanding of the mechanical integrity of the injection/storage system. Based on evaluations for the Northern Lights Carbon Capture and Storage (CCS) project, we focus on thermal effects induced on the caprock via conduction from cooling in the storage sands below. We investigate, using both analytical and numerical approaches, how undrained effects within the low permeability caprock can lead to volumetric contraction differences between the rock framework and the pore fluid which induce both stress and pore pressure changes that must be properly quantified. We show that such undrained effects, while inducing a more complicated response in the stress changes in the caprock, do not necessarily lead to unfavourable tensile conditions, and may, in fact, lead to increases in effective stress. These observations build confidence in the integrity of the caprock/seal system. We also show, through conservative assumptions, that pressure communication between the caprock and storage sands may lead to a localised negative effective stress condition, challenging stability of the base caprock, which will be mitigated for in field development planning.