  We study the process of spinodal decomposition in a scalar quantum field
theory that is quenched from an equilibrium disordered initial state at $T_i >
T_f$ to a final state at $T_f \approx 0$. The process of formation and growth
of correlated domains is studied in a Hartree approximation. We find an
approximate scaling law for the size of the domains $\xi_D(t) \approx \sqrt{t
\xi_0}$ at long times for weakly coupled theories, with $\xi_0$ the zero
temperature correlation length.
