  We derive constraints on the mass-temperature relation of galaxy clusters
from their observed luminosity-temperature relation and X-ray temperature
function. Adopting the isothermal gas in hydrostatic equilibrium embedded in
the universal density profile of dark matter halos, we compute the X-ray
luminosity for clusters as a function of their hosting halo mass. We find that
in order to reproduce the two observational statistics, the mass-temperature
relation is very tightly constrained as T_{gas} = (1.5~2.0)keV
(M_{vir}/10^{14}h_{70}^{-1}M_\odot)^{0.5~0.55}, and a simple self-similar
evolution model (T_{gas} \propto M_{vir}^{2/3}) is strongly disfavored. In the
cosmological model that we assume (a \Lambda CDM universe with \Omega_0=0.3,
\lambda_0=0.7 and h_{70}=1), the derived mass-temperature relation suggests
that the mass fluctuation amplitude \sigma_8 is 0.7--0.8.
