  We analyze how the logarithmic renormalizations in the Cooper channel affect
the non-analytic temperature dependence of the specific heat coefficient \gamma
(T) - \gamma (0)=A(T)T in a 2D Fermi liquid. We show that A(T) is expressed
exactly in terms of the fully renormalized backscattering amplitude which
includes the renormalization in the Cooper channel. In contrast to the 1D case,
both charge and spin components of the backscattering amplitudes are subject to
this renormalization. We show that the logarithmic renormalization of the
charge amplitude vanishes for a flat Fermi surface, when the system becomes
effectively one-dimensional.
