Climate change is expected to increase regional and global air temperatures and significantly alter precipitation regimes. These projected changes in meteorological conditions will likely influence subsurface thermal regimes. Increases in groundwater and soil temperatures could impact groundwater quality, harm groundwater-sourced ecosystems, and contribute to the geotechnical failure of critical infrastructure. Furthermore, permafrost thaw induced by rising subsurface temperatures will likely alter surface and subsurface hydrology in high altitude and latitude regions and exacerbate the rate of anthropogenic climate change by releasing stored carbon into the atmosphere. This contribution discusses the theory and development of governing heat transport equations for cold and temperate regions. Analytical solutions to transient forms of the conduction equation and the conduction–advection equation with and without freezing are detailed. In addition, recently developed groundwater flow and heat transport models that can accommodate freezing and thawing processes are briefly summarized. These models can be applied to simulate climate change-induced permafrost degradation and dormant aquifer activation in cold regions. Several previous reviews have focused on the impact of climate change on subsurface hydraulic regimes and groundwater resources, but this is the first synthesis of the analytical and numerical simulation approaches that have been utilized to investigate the impact of future climate change on subsurface thermal regimes. The current gaps in this body of knowledge are highlighted, and recommendations are made for improving future studies by linking atmospheric global climate models to subsurface heat transport models that consider heat advection via groundwater flow.