  The Carina Nebula complex (CNC) represents one of the most massive
star-forming regions in our Galaxy and shows strong feedback from the high
massive stars. We use our Herschel FIR observations to study the properties of
the clouds over the entire area of the CNC. The good angular resolution of the
Herschel maps corresponds to physical scales of 0.1 - 0.4 pc, and allows us to
analyze the small-scale structures of the clouds. The full extent of the CNC
was mapped with PACS and SPIRE from 70 to 500 micron. We determine temperatures
and column densities at each point in this maps by modeling the observed FIR
SEDs. We also derive a map showing the strength of the UV field. We investigate
the relation between the cloud properties and the spatial distribution of the
high-mass stars, and compute total cloud masses for different density
thresholds. Our Herschel maps resolve, for the first time, the small-scale
structure of the dense clouds. Several particularly interesting regions,
including the prominent pillars south of eta Car, are analyzed in detail. We
compare the cloud masses derived from the Herschel data to previous mass
estimates based on sub-mm and molecular line data. Our maps also reveal a
peculiar "wave"-like pattern in the northern part of the Carina Nebula.
Finally, we characterize two prominent cloud complexes at the periphery of our
Herschel maps, which are probably molecular clouds in the Galactic background.
We find that the density and temperature structure of the clouds in most parts
of the CNC is dominated by the strong feedback from the numerous massive stars,
rather than random turbulence. Comparing the cloud mass and the star formation
rate derived for the CNC to other Galactic star forming regions suggests that
the CNC is forming stars in an particularly efficient way. We suggest this to
be a consequence of triggered star formation by radiative cloud compression.
