Method for treating material formed/found at the bottom of a ladle furnace is provided. The material includes white slag containing lime or lime-based compounds and also includes a metal alloy in the molten or semi-molten/viscous state. The material at the outlet of the ladle furnace cools for a period of time less than about 30-45 minutes.

An apparatus for cooling a material includes: at least one reactor, substantially tubular, which is rotatable and which includes a rotating tubular structure defining inside it a chamber for receiving and passing through the material to be cooled; and means for indirectly cooling the material passing through said chamber by means of a cooling fluid, the means for indirect cooling comprise at least one dispensing device for the cooling fluid. The at least one dispensing device includes at least two dispensing mouths defined by respective slots, with substantially longitudinal development, for the escape of the refrigerant fluid, the device being arranged with respect to the tubular structure in so that the flow outgoing from said two slits affects and laps two respective areas, distinct from each other, of the external surface of the tubular structure.