Higher order contributions in finite temperature renormalization group

We apply to the O(N) λφ4 model the finite temperature renormalization group method, in which the temperature-dependent effective coupling constant and mass are introduced. It is pointed out that the improvement by use of the two-loop renormalization-group coefficients is important at high temperature and drastically changes the lowest order result. We also show that the two-loop renormalization-group coefficients are exact in the large-N limit. (orig.)