The Zakharov system describes the coupled dynamics of the electric field amplitude and the low frequency fluctuation of the ions in a unmagnetized or weakly magnetized plasma. This system couples Schrdinger-like and wave equations and in its physical derivation depends on a parameter $\alpha$ : Large value of $\alpha$ describes a plasma that is very hot, so it is meaningful to study the limit for the solutions to this system as $\alpha$ goes to infinity. In this talk we give rigorous mathematical result in this direction.