  In weakly perturbed systems that are close to integrability, thermalization
can be delayed by the formation of prethermalization plateaus. We study the
build-up of density-density correlations after a weak interaction quench in the
Hubbard model in $d > 1$ dimensions using unitary perturbation theory. Starting
from a pre-quench state at temperature $T$, we show that the prethermalization
values of the post-quench correlations are equal to the equilibrium values of
the interacting model at the same temperature $T$. This is explained by the
local character of density-density correlations.
