  We consider a two-dimensional electron system with Coulomb interaction
between particles at a finite temperature T. We show that the dynamic Kohn
anomaly in the response function at 2K_F leads to a linear-in-T correction to
the spin susceptibility, same as in systems with short-range interaction.
  We show that the singularity of the Coulomb interaction at q=0 does not
invalidate the expansion in powers of r_s, but makes the expansion
non-analytic. We argue that the linear temperature dependence is consistent
with the general structure of Landau theory and can be viewed as originating
from the non-analytic component of the Landau function near the Fermi surface.
