  We use the observed evolution of the galaxy cluster X-ray integral
temperature distribution function between z=0.05 and z=0.32 in an attempt to
constrain the value of the density parameter, Omega_0, for both open and
spatially-flat universes. We conclude that when all the most important sources
of possible error, both in the observational data and in the theoretical
modelling, are taken into account, an unambiguous determination of Omega_0 is
not feasible at present. Nevertheless, we find that values of Omega_0 around
0.75 are most favoured, with Omega_0<0.3 excluded with at least 90 per cent
confidence. In particular, the Omega_0=1 hypothesis is found to be still
viable.
