  We report on experimental determinations of the temperature field in the
interior (bulk) of turbulent Rayleigh-Benard convection for a cylindrical
sample with aspect ratio (diameter over height) of 0.50, both in the classical
and in the ultimate state. The Prandtl number was close to 0.8. We find a
"logarithmic layer" in which the temperature varies as A*ln(z/L) + B with the
distance z from the bottom plate of the sample. The amplitude A varies with
radial position r. In the classical state these results are in good agreement
with direct numerical simulations (DNS); in the ultimate state there are as yet
no DNS. A close analogy between the temperature field in the classical state
and the "Law of the Wall" for the time-averaged down-stream velocity in shear
flow is discussed.
