We analyse the new ISCCP (International Satellite Cloud Climatology Project) D2 cloud data to ascertain if a connection between cosmic-ray flux and cloud cover exists. Despite a previous finding that total-cloud factor and cosmic-ray fluxes were correlated, our results indicate that only the low-level cloud follows solar activity over the full period, 1983-94. Using several proxies for solar activity and the radiative forcing calculated by Ockert-Bell (1992) for the ISCCP cloud types, we estimate the possible impact that such a solar-terrestrial connection may have on climate. We conclude that, possibly excluding the most recent decades, much of the warming of the past century can be quantitatively accounted for by the direct and indirect effects of solar activity.