  This paper deals with the approximation of the weak solutions of the
incompressible Navier Stokes Fourier system. In particular it extends the
artificial compressibility method for the Leray weak solutions of the Navier
Stokes equation, used by Temam, in the case of a bounded domain and later in
the case of the whole space. By exploiting the wave equation structure of the
pressure of the approximating system the convergence of the approximating
sequences is achieved by means of dispersive estimate of Strichartz type. It
will be proved that the projection of the approximating velocity fields on the
divergence free vectors is relatively compact and converges to a weak solution
of the incompressible Navier Stokes Fourier system.
