  The optimized perturbation theory (OPT) at finite temperature recently
developed by the present authors is reviewed by using O(N) phi^4 theory with
spontaneous symmetry breaking. The method resums automatically higher loops
(including the hard thermal loops) at high $T$ and simultaneously cures the
problem of tachyonic poles at relatively low $T$. We prove 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 satisfied for arbitrary $N$ and for any given order of OPT.
