  We consider a two flavor Polyakov--Nambu--Jona-Lasinio (PNJL) model where the
Lagrangian includes an interaction term that explicitly breaks the U$_A(1)$
anomaly. At finite temperature, the restoration of chiral and axial symmetries,
signaled by the behavior of several observables, is investigated. We compare
the effects of two regularizations at finite temperature, one of them, that
allows high momentum quarks states, leading to the full recovery of chiral
symmetry. From the analysis of the behavior of the topological susceptibility
and of the mesonic masses of the axial partners, it is found in the SU(2) model
that, unlike the SU(3) results, the recovery of the axial symmetry is not a
consequence of the full recovery of the chiral symmetry. Thus, one needs to use
an additional idea, by means of a temperature dependence of the anomaly
coefficient, that simulates instanton suppression effects.
