Method of producing a micro-alloyed steel, particularly a tube steel, wherein a cast slab runs through a plant which in conveying direction of the slab comprises, in this sequence, a casting machine, a first furnace, at least one roughing stand, a second furnace, at least one finishing rolling stand and a cooling path, wherein the method comprises: a) definition of a desired temperature profile for the slab over the transit thereof through the plant; b) positioning of at least two temperature-influencing elements (9, 10) for temperature-influencing of the slab in accordance with the defined temperature profile in the process line of the plant, wherein the temperature-influencing elements (9, 10) are inserted between the first furnace and the at least one roughing stand and between the second furnace and the at least one finishing rolling stand; and c) production of the slab or of the strip in the thus-configured plant, wherein the temperature-influencing elements (9, 10) are so operated that the defined temperature profile is at least largely maintained, wherein through use of a temperature-influencing element in the form of cooling means an entry temperature of such depth is achieved in the at least one finishing rolling stand that recrystallisation and grain growth are largely suppressed there, wherein the temperature level between the entry into the at least one roughing stand and the entry into the temperature-influencing element in the form of cooling means aa) is either - particularly for tube steels with low contents of micro-alloyed elements and low slab thicknesses - lowered by means of a temperature-influencing element in the form of cooling means in order to reduce the grain size on entry into the finishing rolling train bb) or - particularly for tube steels with high contents of micro-alloyed elements and large slab thicknesses - raised by means of a temperature-influencing element in the form of heating means in order to ensure complete recrystallisation when roughing takes place. a) definition of a desired temperature profile for the slab over the transit thereof through the plant; b) positioning of at least two temperature-influencing elements (9, 10) for temperature-influencing of the slab in accordance with the defined temperature profile in the process line of the plant, wherein the temperature-influencing elements (9, 10) are inserted between the first furnace and the at least one roughing stand and between the second furnace and the at least one finishing rolling stand; and c) production of the slab or of the strip in the thus-configured plant, wherein the temperature-influencing elements (9, 10) are so operated that the defined temperature profile is at least largely maintained, wherein aa) is either - particularly for tube steels with low contents of micro-alloyed elements and low slab thicknesses - lowered by means of a temperature-influencing element in the form of cooling means in order to reduce the grain size on entry into the finishing rolling train bb) or - particularly for tube steels with high contents of micro-alloyed elements and large slab thicknesses - raised by means of a temperature-influencing element in the form of heating means in order to ensure complete recrystallisation when roughing takes place.