  The linear O($N$) sigma model undergoes a symmetry restoring phase transition
at finite temperature. We show that the nonlinear O($N$) sigma model also
undergoes a symmetry restoring phase transition; the critical temperatures are
the same when the linear model is treated in mean field approximation and the
nonlinear model is treated to leading plus subleading order in the 1/$N$
expansion. We also carefully define and study the behavior of $f_{\pi}$ and the
scalar condensate at low temperatures in both models, showing that they are
independent of field redefinition.
