  Through a 3d-modeling of ASCA observations, we performed a spatially resolved
X-ray spectroscopic study, extending to radii exceeding 150 kpc, for a sample
of 9 groups of galaxies. Combined with published ROSAT results, we conclude
that these systems generally exhibit a strong temperature decline at outer
radii. In our best case, NGC3268, this corresponds to a flattening of the
entropy profile at a level of ~400 keV cm^2. This value is high compared both
to the observed entropy floor of ~100 keV cm^2 and to the expected value from
gravitational heating. We suggest that the observed entropy profile in most
groups at densities exceeding 500 times the critical is purely driven by
non-gravitational heating processes. After comparison with a larger sample of
groups and clusters, we conclude that there is a variation in the level of
non-gravitational heating between ~100 keV cm^2 and ~400 keV cm^2 within every
system. Using models of cluster formation as a reference frame, we established
that the accreted gas reaches an entropy level of 400 keV cm^2 by redshift
2.0-2.5, while such high entropies where not present at redshifts higher than
2.8-3.5, favoring nearly instantaneous preheating. Adopting galactic winds as a
source of preheating, and scaling the released energy by the observed metal
abundance, the variation in the preheating could be ascribed mostly to
variation in the typical overdensity of the energy injection, ~30 for an
entropy floor (100 keV cm^2) and to ~5 for an entropy of 400 keV cm^2.
