We construct two effective lagrangians which reproduce the explicit fl
avor SU(3) symmetry breaking and the trace and axial anomalies of QCD.
All analytical expressions are derived for a hot strange matter but t
he results are only shown for zero baryonic density. We study the coup
ling of the quark condensates (u and s) to the gluon condensate. We al
so consider the temperature behavior of the pion and of the kaon masse
s. We show that the results crucially depend on the choice of the two
free parameters of the model: the chiral transition can be of first or
of second order; the coupling between the gluon and the quark condens
ates can be large or not; the meson masses can increase or decrease wi
th temperature. The introduction of the QCD trace anomaly in the SU(3)
NJL model kills the predictive character of the NJL.