A method of casting steel at a lower overheated temperature during continuous casting, wherein the inner surface of a tundish is heated to a temperature which approximately corresponds to the temperature of the steel in a ladle, the tundish is filled with steel, and the steel is poured into at least one mold. According to the invention a discharge spout of the tundish which opens above the reference level of the metal bath, prior to casting and during heating of the tundish is brought into a position which occupies the lowest point of the inner surface of the tundish, the heating of the tundish is continued until adjusting an approximately stationary thermal gradient between the inner and the outer surfaces of the tundish, and prior to pouring of the steel into the mold the tundish is brought into its casting position.The tundish for the pouring of steel during continuous casting comprises a substantially troughlike lower portion and a domed cover member, at least one bottom nozzle provided for the tundish lower portion, said cover member being provided with an opening for the pouring in of the steel melt from a ladle, and a heating device is arranged above the reference bath level of the tundish. The tundish has a lining possessing a heat conductivity resistance of at least 0.25 m.sup.2.h. .degree.C/Kcal, and is further provided with a discharge spout partially possessing a substantially tubular-shaped cross-section and opening above the reference level of the metal bath. There is also provided means for displacing the tundish about a horizontal axis.