  The presence of undamped harmonic center of mass oscillations of a weakly
interacting Bose gas in a harmonic trap is demonstrated within the dielectric
formalism for a previously introduced finite temperature approximation
including exchange. The consistency of the approximation with the Kohn theorem
is thereby demonstrated. The Kohn modes are found explicitly, generalizing an
earlier zero-temperature result found in the literature. It is shown how the
Kohn mode disappears from the single-particle spectrum, while remaining in the
density oscillation spectrum, when the temperature increases from below to
above the condensation temperature.
