  We study the temperature-filling phase diagram of the single-band Holstein
model in two dimensions using the self-consistent Migdal approximation, where
both the electron and phonon self-energies are treated on an equal footing. By
employing an efficient numerical algorithm utilizing fast Fourier transforms to
evaluate momentum and Matsubara frequency summations, we determine the
charge-density-wave (CDW) and superconducting transition temperatures in the
thermodynamic limit using lattice sizes that are sufficient to eliminate
significant finite size effects present at lower temperatures. We obtain the
temperature-filling phase diagrams for a range of coupling strengths and phonon
frequencies for the model defined on a square lattice with and without
next-nearest neighbor hopping. We find the appearance of a superconducting dome
with a critical temperature that decreases before reaching the
$\mathbf{q}_{\text{max}} = (\pi,\pi)$ CDW phase boundary. For very low phonon
frequencies, we also find an incommensurate CDW phase with the ordering vector
$\mathbf{q}_{\text{max}} \approx (\pi,\pi)$ appearing between the commensurate
CDW and superconducting phases. Our numerical implementation can be easily
extended to treat momentum-dependent electron-phonon coupling, as well as
dispersive phonon branches, and has been made available to the public.
