  We compare predictions of cooled masses and cooling rates from three
stripped-down Semi-Analytic Models (SAMs) of galaxy formation with the results
of N-body+SPH simulations with gas particle mass of 3.9x10^6 Msun, where
radiative cooling of a gas of primordial composition is implemented. We also
run a simulation where cooling is switched on at redshift ~2, in order to test
cooling models in a regime in which their approximations are expected to be
valid. We confirm that cooling models implemented in SAMs are able to predict
the amount of cooled mass at z=0 to within ~20 per cent. However, some relevant
discrepancies are found. (i) When the contribution from poorly resolved halos
is subtracted out, SAMs tend to under-predict by ~30 per cent the mass that
cools in the infall-dominated regime. (ii) At large halo masses SAMs tend to
over-predict cooling rates, though the numerical result may be affected by the
use of SPH. (iii) As found in our previous work, cooling rates are found to be
significantly affected by model details: simulations disfavour models with
large cores and with quenching of cooling at major mergers. (iv) When cooling
is switched on at z~2, cold gas accumulates very quickly in the simulated
halos. This accumulation is reproduced by SAMs with varying degrees of
accuracy.
