  We study a Bose-Einstein condensate (BEC) of a dilute gas with dipolar
interactions, at finite temperature, using the Hartree-Fock-Bogoliubov (HFB)
theory within the Popov approximation. An additional approximation involving
the dipolar exchange interaction is made to facilitate the computation. We
calculate the temperature dependence of the condensate fraction of a condensate
confined in a cylindrically symmetric harmonic trap. We show that the
bi-concave shaped condensates found in Ref. \cite{Ronen07} in certain pancake
traps at zero temperature, are also stable at finite temperature. Surprisingly,
the dip in the central density of these structured condensates is actually
enhanced at low finite temperatures. We explain this effect.
