  In this paper we propose a mathematical model of phase separation for a
quasi-incompressible binary mixture where the spinodal decomposition is induced
by an heat flux governed by the Cattaneo-Maxwell equation. As usual, the phase
separation is considered in the framework of phase field modeling so that the
transition is described by an additional field, the concentration c. The
evolution of concentration is described by the Cahn-Hilliard equation and in
our model is coupled with the Navier-Stokes equation. Since thermal effect are
included, the whole set of evolution equations is set up for the velocity, the
concentration, the temperature and the heat flux. The model is compatible with
thermodynamics and a maximum theorem holds.
