The shell temperature profile varies with the kiln process (precalciner, preheater, long dry, wet etc.), type of refractories installed (due to different conductivities), the residual thickness of the refractories (which reduces with wear during service), and the thickness of coating on the refractories (which changes dependent on process conditions).
For an in-line calciner kiln I would expect shell temperatures of around 200 degrees C for the first 30 per cent of the kiln length where you will have the more insulating refractories installed. The girth gear will be in the region and the shell at this approximate temperature. I would then expect the shell temperature to rise to around 300 degrees C in the upper transition zone from 30 to 60 per cent of the kiln length. The refractories are likely to have little coating in this area. In the burning zone from 60 to 90 per cent of kiln length the shell temperature will be very variable due to coating formation. It could be as low as 150 degrees, but if the coating breaks away and the residual lining thickness is low then it could rise to over 400 degrees.