1. An arrangement for the heating or cooling of conditioned rooms in appartments (201), greenhouses (101) or the like with pipes or pipe members (106, 107; 206, 207) which are arranged in the rooms and through which water, as the heat transfer fluid, flows in order to radiate or absorb heat and which may be connected in a reversible manner to the heat radiating side of a heat pump (125; 225) or, where appropriate, may be connected in a reversible manner by way of a circulatory system to a heat insulated warm water store (240) which may be supplied by the heat pump, and to a heat exchanger (114; 214) which is in direct heat exchange with the surrounding ground and may be connected to the heat absorbing side of the heat pump by way of a circulatory system containing water as the heat transfer fluid, characterized in that a ground tank (114; 214) having a sufficient volume to form heat layers is provided as the heat exchanger in direct heat exchange with the surrounding ground ; in that a second tank (118; 218), which may be insulated from its surroundings and having a sufficient volume to form heat layers, is provided in the direction of flow downstream of the pipes or pipe members (106, 107; 206, 207) ; in that the cold layer region of the second tank (118; 218) is connected to the warm layer region of the first tank (114; 214) by a loop circuit (122, 123; 223) formed according to the type of connecting pipes and in that - for cooling, the cold layer region of the first tank (114; 214) is connected in a reversible manner directly to the pipes or pipe members (106, 107; 206, 207) and to the warm layer region of the second tank (118; 218) disposed downstream in the direction of flow and - for heating, the warm layer region of the second tank (118; 218) is connected in a reversible manner either directly to the pipes or pipe members (106, 107; 206, 207) or to the heat absorbing side of the heat pump (125, 225) and to the cold layer region of the first tank (114; 214) so as to form a closed circuit.