Evolution of the cluster temperature function is extremely sensitive to the mean matter density of the universe .
Current measurements based on cluster temperature surveys indicate that \Omega _ { M } \approx 0.3 with a 1 \sigma statistical error \sim 0.1 , but the systematic errors in this method are of comparable size .
Many more high- z cluster temperatures will be arriving from Chandra and XMM in the near future .
In preparation for future cluster temperature surveys , this paper analyses the cluster mass-temperature relation , with the intention of identifying and reducing the systematic errors it introduces into measurements of cosmological parameters .
We show that the usual derivation of this relation from spherical top-hat collapse is physically inconsistent and propose a more realistic derivation based on a hierarchical merging model that more faithfully reflects the gradual ceasing of cluster evolution in a low- \Omega _ { M } universe .
We also analyze the effects of current systematic uncertainties in the M _ { vir } { - } T _ { X } relation and show that they introduce a systematic uncertainty of \sim 0.1 in the best-fitting \Omega _ { M } .
Future improvements in the accuracy of the M _ { vir } { - } T _ { X } relation will most likely come from comparisons of predicted cluster temperature functions with temperature functions derived directly from large-scale structure simulations .