To obtain a steel material excellent in the surface quality by preventing a red brittleness developed caused by concentration-melting of Cu mixed in the steel onto the surface in hot rolling, in the case of using scrap as an iron-source.

In a method for heating the steel material containing 0.05-3 mass% Cu precedent to the hot-rolling, the steel material is heated in an auxiliary atmosphere having ≤ 5 vol% steam under state of the lowest temperature of the steel material surface at ≥ 1,080°C. Further, in the method, the heating of the steel material is repeatedly performed with at least one time, to the performance of the heating with combustion gas and the heating in the oxidizing atmosphere having ≤ 5% vol% steam during not shorter time t (min) shown in the following relation with the lowest temperature T(K) on the steel material surface under state of the temperature at ≥ 1,080°C, at least one time, respectively. Log10(t) = -0.00301 × (T - 273) + 4.01.

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