The oxygen isotope ratio 18O/16O (expressed as a δ18OVSMOW value) in marine sedimentary rocks has increased by ~8‰ from the early Paleozoic to modern times. Interpretation of this trend is hindered by ambiguities in the temperature of formation of the carbonate, the δ18Oseawater, and the effects of postdepositional diagenesis. Carbonate clumped isotope measurements, a temperature proxy, offer constraints on this problem. This thermometer is thermodynamically controlled in cases where carbonate achieves an equilibrium internal distribution of isotopes and is independent of the δ18O of the water from which the carbonate grew; therefore, it has a relatively rigorous chemical-physics foundation and can be applied to settings where the δ18O of the water is not known. We apply this technique to an exceptionally well-preserved Ordovician carbonate record from the Baltic Basin and present a framework for interpreting clumped isotope results and for reconstructing past δ18Oseawater. We find that the seawater in the Ordovician had lower δ18Oseawater values than previously estimated, highlighting the need to reassess climate records based on oxygen-isotopes, particularly where interpretations are based on assumptions regarding either the δ18Oseawater or the temperature of deposition or diagenesis. We argue that an increase in δ18Oseawater contributed to the long-term rise in the δ18O of marine sedimentary rocks since the early Paleozoic. This rise might have been driven by a change in the proportion of high- versus low-temperature water-rock interaction in the earth's hydrosphere as a whole.