The 18O/16O ratio of cherts (δ18Ochert) increases nearly monotonically by ~15‰ from the Archean to present. Two end-member explanations have emerged: cooling seawater temperature (TSW) and increasing seawater δ18O (δ18Osw). Yet despite decades of work, there is no consensus, leading some to view the δ18Ochert record as pervasively altered. Here, we demonstrate that cherts are a robust archive of diagenetic temperatures, despite metamorphism and exposure to meteoric fluids, and show that the timing and temperature of quartz precipitation and thus δ18Ochert are determined by the kinetics of silica diagenesis. A diagenetic model shows that δ18Ochert is influenced by heat flow through the sediment column. Heat flow has decreased over time as planetary heat is dissipated, and reasonable Archean-modern heat flow changes account for ~5‰ of the increase in δ18Ochert, obviating the need for extreme TSW or δ18Osw reconstructions. The seawater oxygen isotope budget is also influenced by solid Earth cooling, with a recent reconstruction placing Archean δ18OSW 5 to 10‰ lower than today. Together, this provides an internally consistent view of the δ18Ochert record as driven by solid Earth cooling over billion-year timescales that is compatible with Precambrian glaciations and biological constraints and satisfyingly accounts for the monotonic nature of the δ18Ochert trend.