  We study the phenomena of radiative-driven shock waves using a semi-analytic
model based on self similar solutions of the radiative hydrodynamic problem.
The relation between the hohlraum drive temperature $T_{\mathrm{Rad}}$ and the
resulting ablative shock $D_S$ is a well-known method for the estimation of the
drive temperature. However, the various studies yield different scaling
relations between $T_{\mathrm{Rad}}$ and $D_S$, based on different simulations.
In [T. Shussman and S.I. Heizler, Phys. Plas., 22, 082109 (2015)] we have
derived full analytic solutions for the subsonic heat wave, that include both
the ablation and the shock wave regions. Using this self-similar approach we
derive here the $T_{\mathrm{Rad}}(D_S)$ relation for aluminium, using the
detailed Hugoniot relations and including transport effects. By our
semi-analytic model, we find a spread of $\approx 40$eV in the
$T_{\mathrm{Rad}}(D_S)$ curve, as a function of the temperature profile's
duration and its temporal profile. Our model agrees with the various
experiments and the simulations data, explaining the difference between the
various scaling relations that appear in the literature.
