  We have observed NGC 1316 (Fornax A) with the ROSAT HRI. In this paper, we
present the results of these observations and we complement them with the
spectral analysis of the archival PSPC data. The spectral properties suggest
the presence of a significant component of thermal X-ray emission (> 60%),
amounting to ~10^{9}Mo of hot ISM. Within 3' from the nucleus of NGC 1316, the
HRI X-ray surface brightness falls as r^{-2}. In the inner ~40", the X-ray
surface brightness is significantly elongated (e ~ 0.3). This flattened X-ray
feature is confirmed by a straightforward statistics test as well as moment
analysis. By comparing the morphology of the X-ray emission with the
distribution of optical dust patches, we find that the X-ray emission is
significantly reduced at the locations where the dust patches are more
pronounced, indicating that at least some of the X-ray photons are absorbed by
the cold ISM. We also compare the distribution of the hot and cold ISM with
that of the ionized gas, using recently obtained Ha CCD data. We find that the
ionized gas is distributed roughly along the dust patches and follows the large
scale X-ray distribution at r > 1' from the nucleus. However, there is no
one-to-one correspondence between ionized gas and hot gas. Both morphological
relations and kinematics suggest different origins for hot and cold ISM. The
radio jets in projection appear to pass perpendicularly through the central
X-ray ellipsoid. Comparison of thermal and radio pressures suggests that the
radio jets are confined by the surrounding hot gaseous medium.
