  We show that the distribution of the sizes and temperatures of clusters can
be used to constrain cosmological models. The size-temperature (ST)
distribution predicted in a flat Gaussian cluster-abundance-normalized
Omega_0=0.3 model agrees well with the fairly tight ST relation observed. A
larger power-spectrum amplitude sigma_8 would give rise to a larger scatter
about the ST relation as would a larger value of Omega_0 and/or long
non-Gaussian high-density tails in the probability density function. For
Gaussian initial conditions, the ST distribution suggests a constraint sigma_8
Omega_0^{0.26} \simeq 0.76. The ST relation is expected to get tighter at high
redshifts. In the process, we derive a simple formula for the halo
formation-redshift distribution for non-Gaussian models. We also suggest that
the discrepancy between the naive zero-redshift ST relation and that observed
may be due, at least in part, to the fact that lower-mass clusters form over a
wider range of redshifts. An Appendix derives an equation for the
formation-redshift distribution of halos.
