A cooling system for a metallurgical furnace includes a plurality of cooling arrangements having each a set of cooling elements arranged to extract heat from the furnace, the cooling elements having each at least one internal cooling channel for a coolant fluid, where the cooling elements are fluidly connected within each cooling arrangement; at least one discharge piping associated with each cooling arrangement for discharging the coolant fluid towards a main collector, where a flow regulating arrangement is serially mounted with the discharge piping and configured to control a flow rate of the coolant fluid therethrough and hence through the cooling arrangement, where the flow regulating arrangement includes a calibrated orifice defining a default, minimal flow cross section for the coolant fluid and a regulating valve selectively operable to define a variable, additional flow cross-section.