  We present an analysis of the constraining power of future measurements of
the Integrated Sachs-Wolfe (ISW) effect on models of the equation of state of
dark energy as a function of redshift, w(z). To achieve this, we employ a new
parameterization of w, which utilizes the mean value of w(z) (<w>) as an
explicit parameter. This helps to separate the information contained in the
estimation of the distance to the last scattering surface (from the CMB) from
the information contained in the ISW effect. We then use Fisher analysis to
forecast the expected uncertainties in the measured parameters from future ISW
observations for two models of dark energy with very different time evolution
properties. For example, we demonstrate that the cross-correlation of Planck
CMB data and LSST galaxy catalogs will provide competitive constraints on w(z),
compared to a SNAP-like SNe project, for models of dark energy with a rapidly
changing equation of state (e.g. 'Kink' models). Our work confirms that, while
SNe measurements are more suitable for constraining variations in w(z) at low
redshift, the ISW effect can provide important independent constraints on w(z)
at high z.
