  The concept of dimensional reduction in the high temperature regime is
generalized to static Green's functions of composite operators that contain
fermionic fields. The recognition of a natural kinematic region where the
lowest Matsubara modes are close to their mass-shell, and the ultraviolet
behavior of the running coupling constant of the original theory are crucial
for providing the necessary scale hierarchy. The general strategy is
illustrated in the asymptotically-free Gross-Neveu model in 1+1 dimensions,
where we verify that dimensional reduction occurs to the leading order in
$g^2(T)$. We also find, in the same model, that the scale parameter
characterizing the dependence on temperature of the coupling constant in the
reduced theory, $\Lambda_T$, is considerably smaller than
$\Lambda_{\bar{\text{MS}}}$. Implications of our results for QCD are also
discussed.
