  It is known since 1980's that the instanton-induced 't Hooft effective
Lagrangian not only can solve the so called $U(1)a$ problem, by making the
$\eta'$ meson heavy etc, but it can also lead to chiral symmetry breaking. In
1990's it was demonstrated that, taken to higher orders, this Lagrangian
correctly reproduces effective forces in a large set of hadronic channels,
mesonic and baryonic ones. Recent progress in understanding gauge topology at
finite temperatures is related with the so called {\em instanton-dyons}, the
constituents of the instantons. Some of them, called $L$-dyons, possess the
anti-periodic fermionic zero modes, and thus form a new version of the 't Hooft
effective Lagrangian. This paper is our first study of a wide set of hadronic
correlation function. We found that, at the lowest temperatures at which this
approach is expected to be applicable, those may be well compatible with what
is known about them based on phenomenological and lattice studies, provided $L$
and $M$ type dyons are strongly correlated.
