  The dual observables as order parameters for center symmetry are tested at
finite isospin chemical potential $\mu_I$ in a Polyakov-loop enhanced chiral
model of QCD with physical quark masses. As a counterpart of the dressed
Polyakov-loop, the first Fourier moment of pion condensate is introduced for
$\mu_I>{m_\pi}/{2}$ under the temporal twisted boundary conditions for quarks.
We demonstrate that this dual condensate exhibits the similar temperature
dependence as the conventional Polyakov-loop. We confirm that its rapid
increase with $T$ is driven by the evaporating of pion condensation. On the
other hand, the dressed Polyakov-loop shows abnormal thermal behavior, which
even decreases with $T$ at low temperatures due to the influence of pion
condensate. We thus argue that in QCD the critical temperature extracting from
a dual observable may have nothing to do with the quark
confinement-deconfinement transition if the quark mass is very small.
