  The formalism of jet modification in the higher twist approach is modified to
describe a hard parton propagating through a hot thermalized medium. The
leading order contribution to the transverse momentum broadening of a high
energy (near on-shell) quark in a thermal medium is calculated. This involves a
factorization of the perturbative process of scattering of the quark from the
non-perturbative transport coefficient. An operator product expansion of the
non-perturbative operator product which represents $\hat{q}$ is carried out and
related via dispersion relations to the expectation of local operators. These
local operators are then evaluated in quenched SU(2) lattice gauge theory.
