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The new determination of the physical size of the Ly$\alpha$ forest cloud from the double quasar Q1343+266AB (Bechtold et al 1994; Crotts et al. 1994) allows us to evaluate the Ly$\alpha$ cloud contribution to the cosmic baryon density $\Omega_{b,Ly\alpha}$, which is estimated to be at least of a $few \times 10^{-3}$ of $\Omega_o$ (critical closure density for the Universe), the same order as that of the damped Ly$\alpha$ or the Lyman limit systems at $z\approx 2.5$. A firm lower bound of the Ly$\alpha$ cloud radius $\approx 40 h^{-1}$kpc infers a lower limit of baryons mass included in the Ly$\alpha$ clouds. The dependence of $\Omega_{b,Ly\alpha}$ on the temperature of the IGM, together with the amount of baryon density allowed from the standard big bang nucleosynthesis, puts strong constraints on the temperature and density parameter space of the IGM at high redshift, in particular, the IGM temperature could not be higher than 10$^6$K in order to keep the baryons from ending in the absorbers seen in QSO spectra ($h=1$, $\Omega_o=1.0$). Gunn-Peterson effect also constrains the IGM physical conditions, but only excludes the lower temperature and higher density region presently. Further improvements of its upper limits will then push the constraint up to $T_I \approx 10^4 $K region, the probable temperature of a photoionized IGM. Majority of the IGM temperature and density parameter space will be covered by these constraints, which no longer depend on the pressure equilibrium between the cloud gas and the IGM as in the pressure confinement model of the Ly$\alpha$ cloud.
