  We report the statistical properties of temperature and thermal energy
dissipation rate in low-Prandtl number turbulent Rayleigh-B\'enard convection.
High resolution two-dimensional direct numerical simulations were carried out
for the Rayleigh number ($Ra$) of $10^{6} \le Ra \le 10^{7}$ and the Prandtl
number ($Pr$) of 0.025. Our results show that the global heat transport and
momentum scaling in terms of Nusselt number ($Nu$) and Reynolds number ($Re$)
are $Nu=0.21Ra^{0.25}$ and $Re=6.11Ra^{0.50}$, respectively, indicating that
the scaling exponents are smaller than those for moderate-Prandtl number fluids
(such as water or air) in the same convection cell. In the central region of
the cell, probability density functions (PDFs) of temperature profiles show
stretched exponential peak and the Gaussian tail; in the sidewall region, PDFs
of temperature profiles show a multimodal distribution at relative lower $Ra$,
while they approach the Gaussian profile at relative higher $Ra$. We split the
energy dissipation rate into contributions from bulk and boundary layers and
found the locally averaged thermal energy dissipation rate from the boundary
layer region is an order of magnitude larger than that from the bulk region.
Even if the much smaller volume occupied by the boundary layer region is
considered, the globally averaged thermal energy dissipation rate from the
boundary layer region is still larger than that from the bulk region. We
further numerically determined the scaling exponents of globally averaged
thermal energy dissipation rates as functions of $Ra$ and $Re$.
