  We study the non-equilibrium dynamics of a symmetry restoring phase
transition in a scalar field theory, the ``system'', linearly coupled to
another scalar field taken as a ``heat bath''. The ``system'' is initially in
an ordered low temperature phase, and the heat bath is at a temperature close
to the critical temperature for the system. We estimate the time at which the
phase transition to the disordered (symmetric) phase takes place. We derive,
and integrate the one-loop effective equations of motion for the order
parameter that include the effects of the heat bath. A semiclassical Langevin
equation is derived and it is found that it contains a non-dissipative,
non-Markovian kernel, the noise term is colored and correlated on time scales
determined by the temperature of the heat bath. The range of validity of the
Langevin equation and a consistent procedure to incorporate corrections are
discussed.
