  Two-dimensional simulations of Rayleigh-B\'enard convection at $Ra =
5\times10^{10}$ show that vertical logarithmic mean temperature profiles can be
observed in regions of the boundary layer where thermal plumes are emitted. The
profile is logarithmic only in these regions and not in the rest of the
boundary layer where it is sheared by the large scale wind and impacted by
plumes. In addition, the logarithmic behavior is not visible in the horizontal
average. The findings reveal that the temperature profiles are strongly
connected to thermal plume emission and support a perception that parts of the
boundary layer can be turbulent, while others are not. The transition to the
ultimate regime, in which the boundary layers are considered to be fully
turbulent, can therefore be understood as a gradual increases in fraction of
the plume-emitting ('turbulent') regions of the boundary layer.
