  We examine the cosmic growth of the red sequence in a cosmological
hydrodynamic simulation that includes a heuristic prescription for quenching
star formation that yields a realistic passive galaxy population today. In this
prescription, halos dominated by hot gas are continually heated to prevent
their coronae from fueling new star formation. Hot coronae primarily form in
halos above \sim10^12 M\odot, so that galaxies with stellar masses \sim10^10.5
M\odot are the first to be quenched and move onto the red sequence at z > 2.
The red sequence is concurrently populated at low masses by satellite galaxies
in large halos that are starved of new fuel, resulting in a dip in passive
galaxy number densities around \sim10^10 M\odot. Stellar mass growth continues
for galaxies even after joining the red sequence, primarily through minor
mergers with a typical mass ratio \sim1:5. For the most massive systems, the
size growth implied by the distribution of merger mass ratios is typically
\sim2\times the corresponding mass growth, consistent with observations. This
model reproduces mass-density and colour-density trends in the local universe,
with essentially no evolution to z = 1, with the hint that such relations may
be washed out by z \sim 2. Simulated galaxies are increasingly likely to be red
at high masses or high local overdensities. In our model, the presence of
surrounding hot gas drives the trends with both mass and environment.
