  We present an algebraic, nondiagrammatic derivation of finite-temperature
second-order many-body perturbation theory [FT-MBPT(2)], using techniques and
concepts accessible to theoretical chemical physicists. We give explicit
expressions not just for the grand potential but particularly for the mean
energy of an interacting many-electron system. The framework presented is
suitable for computing the energy of a finite or infinite system in contact
with a heat and particle bath at finite temperature and chemical potential.
FT-MBPT(2) may be applied if the system, at zero temperature, may be described
using standard (i.e., zero-temperature) second-order many-body perturbation
theory [ZT-MBPT(2)] for the energy. We point out that in such a situation,
FT-MBPT(2) reproduces, in the zero-temperature limit, the energy computed
within ZT-MBPT(2). In other words, the difficulty that has been referred to as
the Kohn--Luttinger conundrum, does not occur. We comment, in this context, on
a "renormalization" scheme recently proposed by Hirata and He.
