The invention relates to a construction (1 ) comprising a building structure (2, 3, 5, 6, 7) and a ground-based heat storage (4). The invention is characterized in that the building structure (2, 3, 5, 6, 7) is located essentially above the ground-based heat storage (4) in the vertical direction and that the building structure (2, 3, 5, 6, 7) has approximately the same or greater expanse than the heat storage (4) in a direction perpendicular to the vertical direction, wherein the building structure comprises at least one house body (2, 3) arranged in connection to the heat storage (4) and an enclosed space (5) located above the heat storage (4) adjacent to the house body (2, 3); wherein the enclosed space (5) has a limiting surface in the form of a wall (7) or a roof (6) being at least partially transparent to solar radiation and being arranged to allow heating of the enclosed space (5) by means of solar radiation; wherein an air heat pump system (21, 22, 23, 24, 26, 27) is arranged in connection to the enclosed space (5); wherein the air heat pump system (21, 22, 23, 24, 26, 27) is adapted to extract heat from the air in the enclosed space (5); wherein the air heat pump system is furthermore adapted to give off heat to both the heat storage (4) and to a heating system and/or domestic hot water system arranged in the house body (2, 3); and wherein the heat storage (4) is located in connection to a ground level in the enclosed space (5).