  We study the structure of the thermal boundary layer (BL) in
Rayleigh-B\'enard convection for Prandtl number ($Pr$) 0.021 by conducting
direct numerical simulations in a two-dimensional square box for Rayleigh
numbers ($Ra$) up to $10^9$. The large-scale circulation in the flow divides
the horizontal plates into three distinct regions, and we observe that the
local thermal BL thicknesses in the plume-ejection region are larger than those
in the plume-impact and shear-dominated regions. Moreover, the local BL width
decreases as $Ra^{-\beta(x)}$, with $\beta(x)$ depending on the position at the
plate. We find that $\beta(x)$ are nearly the same in impact and shear regions
and are smaller than those in the ejection region. Thus, the local BL width
decreases faster in the ejection region than those in the shear and impact
regions, and we estimate that the thermal BL structure would be uniform
throughout the horizontal plate for $Ra \geq 8 \times 10^{12}$ in our low-$Pr$
convection. We compare the thermal BL profiles measured at various positions at
the plate with the Prandtl-Blasius-Pohlhausen (PBP) profile and find deviations
everywhere for all the Rayleigh numbers. However, the dynamically-rescaled
profiles, as suggested by Zhou \& Xia ({\it Phys. Rev. Lett.}, vol. 104, 2010,
104301), agree well with the PBP profile in the shear and impact regions for
all the Rayleigh numbers, whereas they still deviate in the ejection region. We
also find that, despite the growing fluctuations with increasing $Ra$, thermal
boundary layers in our low-$Pr$ convection are transitional and not yet fully
turbulent.
