  The Euclidean-time hadronic current correlation functions, $G_P(\tau, T)$ and
$G_V(\tau, T)$, of pseudoscalar and vector currents have recently been
calculated in lattice simulations of QCD and have been used to obtain the
corresponding spectral functions. We have used the Nambu-Jona-Lasinio (NJL)
model to calculate such spectral functions, as well as the Euclidean-time
correlators, and have made a comparison to the lattice results for the
correlators. We find evidence for the type of temperature dependence of the NJL
coupling parameters that we have used in previous studies of the mesonic
confinement-deconfinement transition. We also see that the spectral functions
obtained when using the maximum-entropy-method (MEM) and the lattice data
differ from the spectral functions that we calculate in our chiral model.
However, our results for the Euclidean-time correlators are in general
agreement with the lattice results, with better agreement when our
temperature-dependent coupling parameters are used than when
temperature-independent parameters are used for the NJL model. We also discuss
some additional evidence for the utility of temperature-dependent coupling
parameters for the NJL model. For example, if the constituent quark mass at T=0
is $352 {MeV}$ in the chiral limit, the transition temperature is $T_c=208
{MeV}$ for the NJL model with a standard momentum cutoff parameter. (If a
Gaussian momentum cutoff is used, we find $T_c=225 {MeV}$ in the chiral limit,
with $m=368 {MeV}$ at T=0.) The introduction of a weak temperature dependence
for the coupling constant will move the value of $T_c$ into the range 150-170
MeV, which is more in accord with what is found in lattice simulations of QCD
with dynamical quarks.
