  It is by now well established that the magnitude of the two-point
angular-correlation function of the cosmic microwave background temperature
anisotropies is anomalously low for angular separations greater than about 60
degrees. Physics explanations of this anomaly typically focus on the properties
of the Universe at the surface of last scattering, relying on the fact that
large-angle temperature fluctuations are dominated by the Sachs-Wolfe effect
(SW). However, these fluctuations also receive important contributions from the
integrated Sachs-Wolfe effect (ISW) at both early (eISW) and late ($\ell$ISW)
times. Here we study the correlations in those large-angle temperature
fluctuations and their relative contributions to $S_{1/2}$ -- the standard
measure of the correlations on large angular scales. We find that in the
best-fitting $\Lambda$CDM cosmology, while the auto-correlation of the early
contributions (SW plus eISW) dominates $S_{1/2}$, there are also significant
contributions originating from cross-terms between the early and late
contributions. In particular, realizations of $\Lambda$CDM with low $S_{1/2}$
are typically produced from a combination of somewhat low pure-early
correlations and accidental cancellations among early-late correlations. We
also find that if the pure $\ell$ISW auto-correlations were the only
contribution to $S_{1/2}$ in $\Lambda$CDM, then the $p$-value of the observed
cut-sky $S_{1/2}$ would be unremarkable. This suggests that physical mechanisms
operating only at or near the last scattering surface could explain the
observed lack of large-angle correlations, though this is not the typical
resolution within $\Lambda$CDM.
