  We compute double-logarithmically enhanced corrections to $\widehat{q}$ at
relative order $O(g^2)$ in the setting of a weakly coupled quark-gluon plasma,
observing how the thermal scale affects the region of phase space, which gives
rise to these corrections. We furthermore clarify how the region of phase from
which these corrections are borne is situated with respect to that from which
the classical corrections arise at relative order $O(g)$. This represents a
significant step towards our eventual goal of understanding which class of
corrections dominate, thereby pushing forward our quantitative grasp on the
phenomenon of jet quenching in heavy-ion collisions.
