I will assume that you are transferring the iron to a ladle from your coreless induction furnace, and that this ladle is the vessel that you referred to in your thread. The temperature of the alumina refractory will be approximately the same as that of the liquid iron. Since the iron is exposed to the atmosphere at the surface of the vessel with no slag to insulate it, there should be a transition zone where a temperature gradient does exist at this surface. This gradient would become larger the longer the liquid sits in the bath. If the vessel is re-filled every eight minutes, then I will also assume that you are teaming the contents of the ladle into a pattern or mold. Since you state that your temperature readings are taken by actually immersing a thermocouple into the bath, it is unlikely that there will be a significant temperature difference between the bottom of the vessel and the point near the surface where you take your readings. And by significant, I mean less than 50 degrees F. So yes, the stream temperature may be slightly hotter than the surface temperature, but the difference is not likely to be significant unless the bath temperature is very close to the solidus temperature.
Maui