  We study energy landscape and dynamics of the three-dimensional Heisenberg
Spin Glass model in the paramagnetic phase, i.e. for temperature $T$ larger
than the critical temperature $T_\mathrm{c}$. The landscape is non-trivially
related to the equilibrium states even in the high-temperature phase, and
reveals an onset of non-trivial behavior at a temperature $T_\mathrm{o}$, which
is also seen through the behavior of the thermoremanent magnetization. We also
find a power-law growth of the relaxation times far from the spin-glass
transition, indicating a dynamical crossover at a temperature $T_\mathrm{d}$,
$T_\mathrm{c}<T_\mathrm{d}<T_\mathrm{o}$. The arising picture is reminiscent of
the phenomenology of supercooled liquids, and poses questions on which
mean-field models can describe qualitatively well the phenomenology in three
dimensions. On the technical side, local energy minima are found with the
Successive Overrelaxation algorithm, which reveals very efficient for energy
minimization in this kind of models.
