  We discuss Tree+SPH simulations of galaxy clusters and groups, aimed at
studying the effect of cooling and non-gravitational heating on observable
properties of the ICM. We simulate at high resolution four halos,with masses in
the range (0.2-4)10^{14}M_sol. We discuss the effects of using different SPH
implementations and show that high resolution is mandatory to correctly follow
the cooling pattern of the ICM. All of our heating schemes which correctly
reproduce the X-ray scaling properties of clusters and groups do not succeed in
reducing the fraction of collapsed gas below a level of 20 (30) per cent at the
cluster (group) scale. Finally, gas compression in cooling cluster regions
causes an increase of the temperature and a steepening of the temperature
profiles, independent of the presence of non-gravitational heating processes.
This is inconsistent with recent observational evidence for a decrease of gas
temperature towards the center of relaxed clusters. Provided these
discrepancies persist even for a more refined modeling of energy feedback, they
may indicate that some basic physical process is still missing in
hydrodynamical simulations.
