  The correspondence between fermi-sea/bose-condensate displacements and the
number-conserving product of two fermi/bose fields is generalised to finite
temperatures. It is shown that the straightforward generalisation that involves
making the sea-bosons participate in the thermodynamic averaging does not work
out. A remedy is found which involves treating the sea-displacement bosons at
zero temperature while all finite temperature effects have to be lumped into
the coefficients. We also show that all the finite temperature dynamical
four-point and six-point functions come out correctly as do some of the
commutation rules involving the fermion/boson product that go through
unscathed. It is also shown that this unusual prescription of leaving out the
sea-bosons from the thermodynamic averaging does in fact reproduce the correct
RPA dielectric function at finite temperature. This article is not however,
critic-proof.
