Abstract: The invention relates to a pipe arrangement (10) for temperature control of a building, having a single feed pipe (12) and a single return pipe (20), that can be used for operating a concrete core activation during the night and for providing additional cooling power for peak load operation during the day. First and second temperature control circuits (26, 28) branch off from said pipes in a known manner. The direction of flow within the feed end segment (16) of the feed pipe (12) and the return end segment (24) of the return pipe (20) can be reversed by means of a changeover valve (42). Said end segments thus take on a feed or a return function, depending on the flow direction. Check valves (38, 40) within the feed and return end segments (16, 24) ensure that the temperature control medium exiting the currently activated temperature control circuit (26 or 28) does not flow into the corresponding non-activated temperature control circuit (28 or 26).