A new model is developed and applied to simulate the Phanerozoic evolution of seawater composition (dissolved Ca, Sr, dissolved inorganic carbon, alkalinity, pH, δ18O), marine carbonates (Sr/Ca, 87Sr/86Sr, δ13C, δ18O), atmospheric CO2 and surface temperature. The marine carbonate records (Sr/Ca, 87Sr/86Sr, δ13C) are used to reconstruct changes in volcanic/tectonic activity and organic carbon burial over the Phanerozoic. Seawater pH is calculated assuming saturation with respect to calcite and considering the changing concentration of dissolved Ca documented by brine inclusion data. The depth of calcite saturation is allowed to vary through time and the effects of changing temperature and pressure on the stability constants of the carbonate system are considered. Surface temperatures are calculated using the GEOCARB III approach considering also the changing flux of galactic cosmic radiation (GCR). It is assumed that GCR cools the surface of the Earth via enhanced cloud formation at low altitudes. The δ18O of marine carbonates is calculated considering the changing isotopic composition of seawater, the prevailing surface temperatures and seawater pH. Repeated model runs showed that the trends observed in the marine δ18O record can only be reproduced by the model if GCR is allowed to have a strong effect on surface temperature. The climate evolution predicted by the model is consistent with the geological record. Warm periods (Cambrian, Devonian, Triassic, Cretaceous) are characterized by low GCR levels. Cold periods during the late Carboniferous to early Permian and the late Cenozoic are marked by high GCR fluxes and low pCO2 values. The major glaciations occurring during these periods are the result of carbon cycling processes causing a draw-down of atmospheric CO2 and a coevally prevailing dense cloud cover at low-altitudes induced by strong GCR fluxes. The two moderately cool periods during the Ordovician - Silurian and Jurassic - early Cretaceous are characterized by both high pCO2 and GCR levels so that greenhouse warming compensated for the cooling effect of low-altitude clouds. The very high Jurassic δ18O values observed in the geological record are caused by low pH values in surface waters rather than cold surface conditions.