Is the Cluster Temperature Function a Reliable Test for Ω₀?

We discuss the evolution of the cluster temperature function (TF) in different scenarios for structure formation. We use the commonly adopted procedure of fitting the model parameters to the local TF data, finding the best fit values and, most of all, the associated statistical errors. These errors yield an uncertainty in the prediction of the TF evolution. We conclude that, at the moment, observations of cluster temperatures at z<=0.5 could provide only a weak test for $\Omega_0$.