To predict the heat flow flux and surface temperature of a molten metal casting mold surface in a non-stationary state by thermocouple gages arranged between the inside surface of the casting mold and water cooling channels and to obtain a molten metal solidified thickness and temperature profile of a solidified shell by executing calculation of heat conduction which adopts the heat flow flux values predicted by a heat transfer inverse question method from casting mold temperature detecting means arranged at plural points in a casting direction as boundary conditions.

The thermocouple signals 14 of the thermocouples 1 embedded into the casting mold 8 spaces between the inside surface 12 of the casting mold and the water cooling channels 13 of the casting molds, the velocity of flow 15 of the water flowing in the water cooling channels 13 and the measured value of water temperature 16 are sent to a computer 17 into which the thermal conductivity 18 of the casting mold material and the installation distances of the thermocouples 1 are already inputted. At this time, the heat flow flux of the casting mold surface and the inside surface temperature of the casting mold are calculated in accordance with the registered values of the thermocouples. Next, the heat flow flux profile in the casting direction and the inside surface temperature profile of the casting mold are determined by using the measured values of the thermocouples arranged at the plural points in the casting direction. A heat conduction equation is solved by the former as the boundary conditions, by which the temperature profile of the molten metal and the solidified shell 11 is determined.