  We study the optimized perturbation theory (OPT) at finite temperature, which
is a self-consistent resummation method. Firstly, we generalize the idea of the
OPT to optimize the coupling constant in lambda phi^4 theory, and give a proof
of the renormalizability of this generalized OPT. Secondly, the principle of
minimal sensitivity and the criterion of the fastest apparent convergence,
which are conditions to determine the optimal parameter values, are examined in
lambda phi^4 theory. Both conditions exhibit a second-order transition at
finite temperature with critical exponent beta = 0.5 in the two-loop
approximation.
