  We investigate the high temperature fate of four dimensional gauge-Yukawa
theories featuring short distance conformality of either interacting or
non-interacting nature. The latter is known as complete asymptotic freedom and,
as templates, we consider non-abelian gauge theories featuring either two
singlet scalars coupled to gauged fermions via Yukawa interactions or two
gauged scalars with(out) fermions. For theories with interacting fixed points
at short distance, known as asymptotically safe, we consider two calculable
examples.
  Exploring the landscape of safe and free theories above we discover a class
of complete asymptotically free theories for which symmetry breaks at arbitrary
high temperatures. In its minimal form this class is constituted by a theory
with two fundamental gauged scalars each gauged under an independent group.
