  Wall-bounded turbulent flows are widely observed in natural and engineering
systems, such as air flows near the Earth's surface, water flows in rivers, and
flows around a car or a plane. The universal logarithmic velocity profile in
wall-bounded turbulent flows proposed by von K\'arm\'an in 1930 is one of the
few exact physical descriptions of turbulence. However, the mean velocity and
temperature profiles cannot be adequately described by this universal log law
when buoyancy effects are present. Monin-Obukhov similarity theory (MOST),
proposed in 1954, has been the cornerstone theory to account for these buoyancy
effects and to describe the atmospheric boundary layer. MOST has been used in
almost all global weather, climate and hydrological models to describe the
dependence of the mean velocity, temperature and scalar profiles on buoyancy.
According to MOST, the logarithmic temperature profile breaks down as buoyancy
effects become important. In contrast, here we show that this long-standing
MOST theory does not apply for temperature. We propose a new theory for the
logarithmic profile of near-wall temperature, which corrects MOST pitfalls and
is supported by both high-resolution direct numerical simulations and field
observations of the convective atmospheric boundary layer. Buoyancy effects do
not modify the logarithmic nature but instead modulate the slope of the
temperature profile compared to the universal von K\'arm\'an slope. The new
formulation has widespread applications such as in climate models, where the
proposed new temperature log law should lead to more realistic continental
surface temperature, which are strongly impacted by buoyancy.
