  We study the renormalization of the O(N) model using the auxiliary field
formalism (Hubbard-Stratonovich transformation) in the 1/N expansion at finite
temperature. We provide the general strategy of renormalization for arbitrary
order, and make calculation up to next-to-leading order. We show that
renormalization is possible for any values of the condensates, prove the
temperature independence of the counterterms and determine the cutoff
dependence of the first nontrivial counterterm parts.
