  We study Landau gauge gluon propagators in two-color QCD at finite quark
chemical potential ($\mu_q$) and temperature ($T$). We include medium
polarization effects at one-loop by quarks into massive gluon propagators, and
compared the analytic results with the available lattice data. We particularly
focus on the high density phase of color-singlet diquark condensates whose
critical temperature is $\sim 100$ MeV with weak dependence on $\mu_q$. At zero
temperature the color singlet condensates protect the IR limit of electric and
magnetic gluon propagators from the medium screening effects. At finite
temperature, this behavior remains true for the magnetic sector, but the
electric screening mass should be generated by thermal, and hence gapless,
particles which are unbound from the diquark condensates. Treating thermal
excitations as quasi-quarks, we found that the electric screening develops too
fast compared to the lattice results. Beyond the critical temperature for
diquark condensates the analytic results are consistent with the lattice
results.
