  Only recently the essential role of the percolation critical point has been
considered on the dynamical properties of connected regions of aligned spins
(domains) after a sudden temperature quench. In equilibrium, it is possible to
resolve the contribution to criticality by the thermal and percolative effects
(on finite lattices, while in the thermodynamic limit they merge at a single
critical temperature) by studying the cluster size heterogeneity,
$H_{\scriptstyle\rm eq}(T)$, a measure of how different the domains are in
size. We here extend this equilibrium measure and study its temporal evolution,
$H(t)$, after driving the system out of equilibrium by a sudden quench in
temperature. We show that this single parameter is able to detect and well
separate the different time regimes, related to the two time scales in the
problem, the short, percolative and the long, coarsening one.
