  We consider the O(N) linear {\sigma} model and introduce an auxiliary field
to eliminate the scalar self-interaction. Using a suitable limiting process
this model can be continuously transformed into the nonlinear version of the
O(N) model. We demonstrate that, up to two-loop order in the CJT formalism, the
effective potential of the model with auxiliary field is identical to the one
of the standard O(N) linear {\sigma} model, if the auxiliary field is
eliminated using the stationary values for the corresponding one- and two-point
functions. We numerically compute the chiral condensate and the {\sigma}- and
{\pi}-meson masses at nonzero temperature in the one-loop approximation of the
CJT formalism. The order of the chiral phase transition depends sensitively on
the choice of the renormalization scheme. In the linear version of the model
and for explicitly broken chiral symmetry, it turns from crossover to first
order as the mass of the {\sigma} particle increases. In the nonlinear case,
the order of the phase transition turns out to be of first order. In the region
where the parameter space of the model allows for physical solutions,
Goldstone's theorem is always fulfilled.
