  An optimized perturbation theory (OPT) at finite temperature T, which resums
higher order terms in the naive perturbation, is developed in O(N) phi^4
theory. It is proved that (i) the renormalization of the ultra-violet
divergences can be carried out systematically in any given order of OPT, and
(ii) the Nambu-Goldstone theorem is fulfilled for arbitrary N and for any given
order of OPT.
  The method is applied for the O(4) sigma model to study the soft modes
associated with the chiral transition in quantum chromodynamics. Threshold
enhancement of the spectral functions at finite T in the scalar and
pseudo-scalar channels is shown to be a typical signal of the chiral
transition.

High Energy Physics - Phenomenology;High Energy Physics - Lattice;High Energy Physics - Theory;Nuclear Theory