  The fate of symmetries at high temperature determines the dynamics of the
very early universe. It is conceivable that temperature effects favor symmetry
breaking instead of restoration. Concerning global symmetries, the non-linear
sigma model is analyzed in detail. For spontaneously broken gauge symmetries,
we propose the gauge boson magnetic mass as a ``flag'' for symmetry
(non)-restoration. We consider several cases: the standard model with one and
two Higgs doublets in the perturbative regime, and the case of a strongly
interacting Higgs sector. The latter is done in a model independent way with
the tools provided by chiral Lagrangians. Our results clearly point towards
restoration, a pattern consistent with recent lattice computations for global
symmetries. In addition, we explicitly verify $BRST$ invariance for gauge
theories at finite temperature.
