  We analyse the high temperature behaviour of softly broken supersymmetric
theories taking into account the role played by effective non-renormalizable
terms generated by the decoupling of superheavy degrees of freedom or the
Planck scale physics. It turns out that discrete or continuous symmetries,
spontaneously broken at intermediate scales, may never be restored, at least up
to temperatures of the cutoff scale. There are a few interesting differences
from the usual non-restoration in non-supersymmetric theories case where one
needs at least two Higgs fields and non-restoration takes place for a range of
parameters only. We show that with non-renormalizable interactions taken into
account the non-restoration can occur for any nonzero range of parameters even
for a single Higgs field. We show that such theories in general solve the
cosmological domain wall problem, since the thermal production of the dangerous
domain walls is enormously suppressed.
