  We report progress towards computing the heavy quark momentum diffusion
coefficient from the correlator of two chromo-electric fields attached to a
Polyakov loop in pure SU(3) gauge theory. Using a multilevel algorithm and
tree-level improvement, we study the behavior of the diffusion coefficient as a
function of temperature in the wide range $1.1 < T / T_c < 10^4$ in order to
compare it to perturbative expansions at high temperature. We find that within
errors the lattice results are remarkably compatible with the next-to-leading
order perturbative result.
