In this paper the problem of energy-optimal heating/cooling a building is considered. Here the given subset of rooms in a building must have given temperatures. It is proven that if heat is supplied from a single heat source then it is optimal to supply it only to the rooms with given temperatures. If individual heat sources (separate air-conditioners/heat pumps in each room) are used then it is more efficient to supply/remove heat to the tar-get rooms and also to intermediate rooms with non-fixed temperatures.