Recent theoretical advances in the relationship between heat transport and the position of the Intertropical Convergence Zone (ITCZ) present an elegant framework through which to interpret past changes in tropical precipitation patterns. Using a very large ensemble of climate model simulations, we investigate whether it is possible to use this framework to interpret changes in the position of the ITCZ in response to glacial and interglacial boundary conditions. We find that the centroid of tropical precipitation, which represents the evolution of precipitation in the whole tropics, is best correlated with heat transport changes. We find that the response of the annual mean ITCZ to glacial and interglacial boundary conditions is quite different to the response of the climatological annual cycle of the ITCZ to the seasonal cycle of insolation. We show that the reason for this is that while the Hadley Circulation plays a dominant role in transporting heat over the seasonal cycle, in the annual mean response to forcing, the Hadley Circulation is not dominant. When we look regionally, rather than at the zonal mean, we find that local precipitation is poorly related either to the zonal mean ITCZ or to meridional heat transport. We demonstrate that precipitation is spatially highly variable even when the zonal mean ITCZ is in the same location. This suggests only limited use for heat transport in explaining local precipitation records; thus, there is limited scope for using heat transport changes to explain individual paleoprecipitation records.