  We have explored the electroweak phase transition in minimal supergravity
models by extending previous analysis of the one-loop Higgs potential to
include finite temperature effects. Minimal supergravity is characterized by
two higgs doublets at the electroweak scale, gauge coupling unification, and
universal soft-SUSY breaking at the unification scale. We have searched for the
allowed parameter space that avoids washout of baryon number via unsuppressed
anomalous Electroweak sphaleron processes after the phase transition. This
requirement imposes strong constraints on the Higgs sector. With respect to
weak scale baryogenesis, we find that the generic MSSM is {\it not}
phenomenologically acceptable, and show that the additional experimental and
consistency constraints of minimal supergravity restricts the mass of the
lightest CP-even Higgs even further to $m_h\lsim 32\GeV$ (at one loop), also in
conflict with experiment. Thus, if supergravity is to allow for baryogenesis
via any other mechanism above the weak scale, it {\it must} also provide for
B-L production (or some other `accidentally' conserved quantity) above the
electroweak scale. Finally, we suggest that the no-scale flipped $SU(5)$
supergravity model can naturally and economically provide a source of B-L
violation and realistically account for the observed ratio $n_B/n_\gamma\sim
10^{-10}$.
