  Using experimental data on thermal convection, obtained at a Rayleigh number
of 1.5 $\times 10^{11}$, it is shown that the temperature structure functions
$<\Delta T_{r}^p>$, where $\Delta T_r$ is the absolute value of the temperature
increment over a distance $r$, can be well represented in an intermediate range
of scales by $r^{\zeta_p} \phi (r)^{p}$, where the $\zeta_p$ are the scaling
exponents appropriate to the passive scalar problem in hydrodynamic turbulence
and the function $\phi (r) = 1-a(\ln r/r_h)^2$. Measurements are made in the
midplane of the apparatus near the sidewall, but outside the boundary layer.
