Geothermal energy, derived from the Earth’s internal heat, can be harnessed due to the geothermal gradient between the Earth’s interior and its surface. This heat, sustained by radiogenic decay, varies across regions, and is highest near volcanic areas. In 2020, 108 countries utilised geothermal energy, with an installed capacity of 15,950 MWe for electricity and 107,727 MWt for direct use in 2019. Low-enthalpy sources require binary systems for power production. Open-loop systems face issues like scaling, difficult water treatment, and potential seismicity, while closed-loop systems, using abandoned petroleum or gas wells, reduce costs and environmental impacts greatly. The novel geothermal gravity heat pipe (GGHP) design eliminates parasitic power consumption by using hydrostatic pressure for fluid circulation. Implemented in an abandoned well in north-east (NE) Slovenia, the GGHP uses a numerical finite difference method to model heat flow. The system vaporises the working fluid in the borehole, condenses it at the surface, and uses gravitational flow for circulation, maintaining efficient heat extraction. The model predicts that continuous maximum capacity extraction depletes usable heat rapidly. Future work will explore sustainable heat extraction and potential discontinuous operation for improved efficiency.