Geothermal energy is increasingly recognized as a useful energy source for both industrial and residential purposes. Disclosed herein are units for subterranean heat exchange comprising a polymer block with ‘mini-channels’ adapted and/or sized for highly efficient heat exchange. In some embodiments such units can, as needed, be manufactured off site, spooled for transport, and conveniently installed in boreholes. Other arrangements are also described for conduits located within a borehole for heat exchange, without a polymer block. Also disclosed are geothermal heat exchange systems including those that employ such units, for example with direct expansion of a two-phase heat-exchange fluid such as carbon dioxide.