  We discuss the (non)-restoration of global and local symmetries at high
temperature. First, we analyze a two-scalar model with $Z_2 \times Z_2$
symmetry using the exact renormalization group. We conclude that inverse
symmetry breaking is possible in this kind of models within the perturbative
regime. Regarding local symmetries, we consider the $SU(2) \otimes U(1)$ gauge
symmetry and focus on the case of a strongly interacting scalar sector.
Employing a model-independent chiral Lagrangian we find indications of symmetry
restoration.
