  We perform an extensive analysis of neutrino diffusion in quark matter within
the MIT bag model at arbitrary temperature and degeneracy. We examine in detail
the contribution of each of the relevant weak interaction processes to the
total neutrino opacity and evaluate the effect of the strange quark mass, the
bag constant, and the QCD perturbative corrections to the MIT bag model. We
also investigate the anisotropic contribution to the neutrino distribution
function in scatterings, the mean energy transfer and the mean scattering
angle. The density and temperature dependence of the diffusion coefficients
$D_n$ that govern the cooling and deleptonization of a compact star is shown in
detail. Finally, our numerical results for the neutrino mean free paths are
compared against known analytic approximations. We conclude that neutrino
scattering constitutes a significant portion of the total neutrino opacity in
leptonized quark matter and neutrino-quark scattering is, in general, very
similar to neutrino-electron scattering with respect to both mean energy
transfer per scattering and mean scattering angle.
