Recent Electric Arc Furnaces are equipped with ultra high power transformers to provide maximum values of electric power and minimize the melting time. The active power is increased by increasing arc length and arc voltage, however in these conditions energy losses due to radiation can also be increased with a consequent decrease in thermal efficiency. The energy radiated from the electric arcs is transferred to the walls inside the EAF promoting hot spots which represent a catastrophic operational condition. This work reports a radiation model which describes the formation of hot spots as a function of arc length and foamy slag height in an industrial EAF of 210 ton. of nominal capacity. Temperature profiles on the surface of the water cooled panels and values for the incident radiation were computed as a function of foamy slag height, used subsequently to define conditions to eliminate the formation of hot spots.