The invention relates to a geothermal insulation system (10) for the insulation of an external surface (16) of a building (12), characterised by comprising: internal insulation panels (24), first internal spacers (22) attaching the internal insulation panels (24) onto the external surface (16) of a wall (14) of the building (12) in the mounted state such that an internal air chamber (20) is left between the internal insulation panels (24) and the external surface (16) of the wall (14), external insulation panels (34), second spacers (32) attaching the external insulation panels (34) onto an external side of the internal insulation panels (24) in the mounted state such that an external air chamber (30) is left between the external insulation panels (34) and the external side of the internal insulation panels (24) and an upper region (31) of the external air chamber (30) is in air communication with an upper region (21) of the internal air chamber (20), a soil-air heat exchanger (44) recessed into the soil, a first air duct (46) connecting the soil-air heat exchanger (44) with the internal air chamber (20), a second air duct (48) connecting the soil-air heat exchanger (44) with the external air chamber (30). The invention further relates to a method for the insulation of an external surface (16) of a building (12) with the use of geothermal energy.