  We present new optical imagery of the X-ray bright elliptical galaxy NGC
5846, the dominant galaxy of a small group of galaxies. A dust lane with a dust
mass of 7 10^3 Msun is detected in the central few kpc of NGC 5846. The
morphology of the dust features are strikingly similar to that observed for the
optical nebulosity AND the X-ray emission. A physical connection between the
different phases of the interstellar medium therefore seems likely.
  We discuss three different options for the origin of the dusty nebular
filaments: Condensation out of a cooling flow, mass loss of late-type stars
within NGC 5846, and material donated by a small neighbouring galaxy. We
conclude that the dust as well as the optical nebulosity are most likely
products of a recent interaction with a small, relatively gas-rich galaxy,
probably of Magellanic type.
  Dust grains in the dust lane are destroyed by sputtering in the hot,
X-ray-emitting gas in less than about 10^7 yr, which is shorter than the
crossing time of a (small) galaxy through the central 5 kpc of NGC 5846. We
argue that the dust is replenished by evaporation of cool, dense gas cloudlets
that were brought in during the interaction. The evaporation rate of cool gas
in NGC 5846, 0.001 solar mass per year, is consistent with the "mass deposition
rate" derived from X-ray measurements.
  The energy lost by the hot gas through heating of dust and evaporation of
cool gas clouds in the central few kpc of NGC 5846 is adequately balanced by
heat sources: transport of heat by electron conduction and loss of kinetic
energy of the in-falling galaxy. There does not seem to be a need to invoke the
presence of a "cooling flow" to explain the X-ray and optical data.
