An electromagnetic induction furnace which is intended to melt at least one electrically conductive material, such as an oxide and/or a metal, and which includes at least one inductor having at least one turn and at least one cooling circuit suitable for cooling at least the inductor. Said furnace is characterized in that the heat-transfer fluid of at least one cooling circuit is supercritical CO2. The invention also relates to a method for operating the furnace and to the use thereof for melting a mixture of metals (steel, zirconium, etc.) with oxides (uranium UO2, zirconium, etc.), as well as concrete components, the mixture representing a corium.