  We discuss the thermodynamics of the O(N) nonlinear sigma model in 1+1
dimensions. In particular we investigate the NLO 1/N correction to the 1PI
finite temperature effective potential expressed in terms of an auxiliary
field. The effective potential contains temperature-dependent divergences which
cannot be renormalized properly. We argue that this problem vanishes at the
minimum of the effective potential. Therefore physical quantities like the
pressure are well defined and can be renormalized in a temperature-independent
way. We give a general argument for the occurrence of temperature-dependent
divergences outside the minimum. We present calculations of the pressure and
show that 1/N is a good expansion. It turns out that the pressure normalized to
that at infinite temperature is N-independent like the flavor independence of
the same quantity in QCD.
