  We investigate the enhancement of lepton number, energy, and entropy
transport resulting from active-sterile neutrino conversion $\nu_e\to\nu_s$
deep in the post-bounce supernova core followed by re-conversion
$\nu_s\to\nu_e$ further out, near the neutrino sphere. We explicitly take
account of shock wave and neutrino heating modification of the active neutrino
forward scattering potential which governs sterile neutrino production. We find
that the $\nu_e$ luminosity at the neutrino sphere could be increased by
between $\sim 10 %$ and $\sim 100 %$ during the crucial shock re-heating epoch
if the sterile neutrino has a rest mass and vacuum mixing parameters in ranges
which include those required for viable sterile neutrino dark matter. We also
find sterile neutrino transport-enhanced entropy deposition ahead of the shock.
This `` pre-heating\rq\rq can help melt heavy nuclei and thereby reduce the
nuclear photo-dissociation burden on the shock. Both neutrino luminosity
enhancement and pre-heating could increase the likelihood of a successful core
collapse supernova explosion.
