For early-type galaxies, the ability to sustain a corona of hot, X-ray-emitting gas could have played a key role in quenching their star formation history. A halo of hot gas may act as an effective shield against the acquisition of cold gas and can quickly absorb stellar mass loss material. Yet, since the discovery by the Einstein Observatory of such X-ray haloes around early-type galaxies, the precise amount of hot gas around these galaxies still remains a matter of debate. By combining homogeneously derived photometric and spectroscopic measurements for the early-type galaxies observed as part of the ATLAS3D integral field survey with measurements of their X-ray luminosity based on X-ray data of both low and high spatial resolution (for 47 and 19 objects, respectively) we conclude that the hot gas content of early-type galaxies can depend on their dynamical structure. Specifically, whereas slow rotators generally have X-ray haloes with luminosity LX, gas and temperature T values that are well in line with what is expected if the hot gas emission is sustained by the thermalization of the kinetic energy carried by the stellar mass loss material, fast rotators tend to display LX, gas values that fall consistently below the prediction of thismodel, with similar T values that do not scale with the stellar kinetic energy (traced by the stellar velocity dispersion) as observed in the case of slow rotators. Such a discrepancy between the hot gas content of slow and fast rotators would appear to reduce, or even disappear, for large values of the dynamical mass (above ∼3× 1011Mȯ), with younger fast rotators displaying also somewhat larger LX, gas values possibly owing to the additional energy input from recent supernovae explosions. Considering that fast rotators are likely to be intrinsically flatter than slow rotators, and that the few LX, gas-deficient slow rotators also happen to be relatively flat, the observed LX, gas deficiency in these objects would support the hypothesis whereby flatter galaxies have a harder time in retaining their hot gas, although we suggest that the degree of rotational support could further hamper the efficiency with which the kinetic energy of the stellar mass loss material is thermalized in the hot gas. We discuss the implications that a different hot gas content could have on the fate of both acquired and internally produced gaseous material, considering in particular how the LX, gas deficiency of fast rotators would make them more capable to recycle the stellar mass loss material into new stars than slow rotators. This would be consistent with the finding that molecular gas and young stellar populations are detected only in fast rotators across the entire ATLAS3D sample, and that fast rotators tend to have a larger specific dust mass content than slow rotators.