  We take advantage of the biggest cosmological simulation to date for a
critical CDM universe in order to test robustness of the cluster mass function
on a range of masses much wider than tested before. On the high mass end our
results show an excess of hot clusters and a milder evolution compared to the
analytical predictions based on the Press & Schechter formula. These features
must be properly taken into account in deriving the cluster X-ray temperature
function at moderate and high redshifts. On a general basis, the reduced
negative evolution in the number of hot clusters could alleviate the
discrepancies between the predictions for critical universes and incoming data,
which instead seem to favour low Omega_0
