  We present a numerical study of the many-body localization (MBL) phenomenon
in the high-temperature limit within an anisotropic Heisenberg model with
random local fields. Taking the dynamical spin conductivity $\sigma(\omega)$ as
the test quantity, we investigate the full frequency dependence of
sample-to-sample fluctuations and their scaling properties as a function of the
system size $L\leq 28$ and the frequency resolution. We identify differences
between the general interacting case $\Delta>0$ and the anisotropy $\Delta=0$,
the latter corresponding to the standard Anderson localization. Except for the
extreme MBL case when the relative sample-to-sample fluctuations became large,
numerical results allow for the extraction of the low-$\omega$ dependence of
the conductivity. Results for the d.c. value $\sigma_0$ indicate a crossover
into the MBL regime, i.e. an exponential-like variation with the disorder
strength $W$. For the same regime, our numerical analysis indicates that the
low-frequency exponent $\alpha$ exhibits a small departure from $\alpha\sim 1$
only.
