  We show that in the Minimal Supersymmetric Standard Model one--loop effects
at finite temperature may lead to a spontaneous breaking of CP invariance in
the scalar sector. Requiring that the breaking takes place at the critical
temperature for the electroweak phase transition, we find that the parameters
space is compatible with a mass of the Higgs pseudoscalar in agreement with the
present experimental lower bounds. Possible implications for baryogenesis are
discussed.
