  Motivated by questions about the QCD deconfining phase transition, we studied
in two previous papers Model A (Glauber) dynamics of 2D and 3D Potts models,
focusing on structure factor evolution under heating (heating in the gauge
theory notation, i.e., cooling of the spin systems). In the present paper we
set for 3D Potts models (Ising and 3-state) the scale of the dynamical effects
by comparing to equilibrium results at first and second order phase transition
temperatures, obtained by re-weighting from a multicanonical ensemble. Our
finding is that the dynamics entirely overwhelms the critical and non-critical
equilibrium effects.
  In the second half of the paper we extend our results by investigating the
Glauber dynamics of pure SU(3) lattice gauge on $N_{\tau} N_{\sigma}^3$
lattices directly under heating quenches from the confined into the deconfined
regime. The exponential growth factors of the initial response are calculated,
which give Debye screening mass estimates. The quench leads to competing vacuum
domains of distinct $Z_3$ triality, which delay equilibration of pure gauge
theory forever, while their role in full QCD remains a subtle question. As in
spin systems we find for pure SU(3) gauge theory a dynamical growth of
structure factors, reaching maxima which scale approximately with the volume of
the system, before settling down to equilibrium. Their influence on various
observables is studied and different lattice sizes are simulated to illustrate
an approach to a finite volume continuum limit. Strong correlations are found
during the dynamical process, but not in the deconfined phase at equilibrium.
