(1 vote from 1 institution)
Observational and numerical studies gave hints that the hot gaseous haloes of ETGs may be sensitive to the galaxy internal kinematics. By using high resolution 2D hydro simulations, and realistic two-component (stars plus dark matter) axisymmetric galaxy models, we study the evolution of the hot haloes in a suite of flat ETGs of fixed mass distribution, but with variable amounts of azimuthal velocity dispersion and rotational support, including the possibility of a counter-rotating inner stellar disc. The hot halo is fed by stellar mass losses and heated by SNIa explosions and thermalization of stellar motions. We measure the value of the thermalization parameter gamma (the ratio between the heating due to the relative velocity between the stellar streaming and the ISM bulk flow, and the heating attainable by complete thermalization of the stellar streaming motions). We find that 1) the X-ray emission and the average temperature are larger in fully velocity dispersion supported systems; 2) 0.1<gamma<0.2 for isotropic rotators (with a trend for being larger for lower dark mass models); 3) systems that are isotropic rotators at large radii with an inner counter-rotating disc, or fully velocity dispersion supported systems with an inner rotating disc, have gamma=1, again with a trend to increase for lower dark mass contents. We also find that the lower X-ray luminosities of isotropic rotators cannot be explained just by their low gamma, but are due to the complicated flow structure, consequence of the angular momentum stored at large radii. X-ray emission weighted temperatures and luminosities nicely match observed values; the X-ray isophotes are boxy in case of significant galaxy rotation. Overall, it is found that rotation has an important role to explain the observational result that more rotationally supported ETGs on average show a lower X-ray emission [abridged].