  Elliptical galaxies have hot coronae with X-ray luminosities and mean gas
temperatures that span over wide ranges. This variation can be partially due to
the energy budget of the hot gas, that depends on the host galaxy structure and
internal kinematics. With the aid of realistic axisymmetric galaxy models, we
performed a diagnostic study focussed on the effects of galaxy flattening and
rotational support on the hot gas temperature.
