  A renormalization group (RG) analysis of the superconductive instability of
an anisotropic fermionic system is developed at a finite temperature. The
method appears a natural generalization of Shankar's approach to interacting
fermions and of Weinberg's discussion about anisotropic superconductors at T=0.
The need of such an extension is fully justified by the effectiveness of the RG
at the critical point. Moreover the relationship between the RG and a
mean-field approach is clarified, and a scale-invariant gap equation is
discussed at a renormalization level in terms of the eigenfunctions of the
interaction potential, regarded as the kernel of an integral operator on the
Fermi surface. At the critical point, the gap function is expressed by a single
eigenfunction and no symmetry mixing is allowed. As an illustration of the
method we discuss an anisotropic tight-binding model for some classes of high
$T_c$ cuprate superconductors, exhibiting a layered structure. Some indications
on the nature of the pairing interaction emerge from a comparison of the model
predictions with the experimental data.
