A system and method supplies users with heat energy or cooling energy via a carrier medium. At least one source of heat energy or chilling energy has an output line that is connected to the input of at least one controllable distributor device. The distributor has a number of outlets, to which the supply lines for users are connected to heating or cooling supplies at various temperature levels. Any of the users may be selected by the distribution device, for supplying carrier medium at the required temperature. At least one heat reservoir is connected in parallel to at least one part of the user for heat energy at different temperature levels, in which the excess heat energy at the given temperature level may be stored and from which the heat energy contained therein may be extracted and supplied to the user with the relevant temperature level.