  We construct the sphaleron solution, at zero and finite temperature, in the
Minimal Supersymmetric Standard Model as a function of the supersymmetric
parameters, including the leading one-loop corrections to the effective
potential in the presence of the sphaleron. At zero temperature we have
included the one-loop radiative corrections, dominated by the top/stop sector.
The sphaleron energy $E_{\rm MSSM}$ mainly depends on an effective Higgs mass
${\displaystyle m_h^{\rm eff}=\lim_{m_A\gg m_W} m_h}$, where $m_h$ is the
lightest CP-even Higgs mass and $m_A$ the pseudoscalar mass. We have compared
it with the Standard Model result, with $m_h^{\rm SM}=m_h^{\rm eff}$, and found
small differences (1-2\%) in all cases. At finite temperature we have included
the one-loop effective potential improved by daisy diagram resummation. The
sphaleron energy at the critical temperature can be encoded in the temperature
dependence of the vacuum expectation value of the Higgs field with an error
$\simlt 10$\%. The light stop scenario has been re-examined and the existence
of a window where baryon asymmetry is not erased after the phase transition,
confirmed. Although large (low) values of $m_h$ ($m_A$) are disfavoured by the
strength of the phase transition, that window (along with LEP results) allows
for $m_h\simlt 80$ GeV, $m_A\simgt 110$ GeV and $A_t\simlt 0.4\; m_Q$.
