= Solution
The geological record is a collection of thermometers with different sampling biases, not a direct time series of the whole mantle.
\b[Primary melt compositions constrain melting temperatures.] Reconstruct <primary magma> compositions from dated, suitably unaltered <basalts> by correcting for <fractional crystallization> and checking equilibrium with <olivine>. Experimental <phase equilibrium> constraints and mineral–melt thermometers then constrain the pressure and temperature of melt generation. In laboratory calibrations, a candidate melt and mineral assemblage are equilibrated at controlled pressure and temperature, quenched, and their crystals and glass analyzed. Repetition across adjacent conditions brackets the relevant <phase equilibrium> boundaries. Correcting for decompression and <latent heat> then allows comparison as <mantle potential temperature>. Age-controlled, non-arc basalt suites are especially valuable for separating changes in ambient mantle from exceptional <mantle plumes>. The 2010 reconstruction by <Claude Herzberg> and colleagues combines this approach with the temporal distribution of high-Mg parental melts.<Thermal history of the Earth and its petrological expression by Claude Herzberg and others>[Sections on primary magma reconstruction and comparison of non-arc basalts with komatiites]{ref}
\b[<Komatiites> provide evidence for unusually hot melting, with qualifications.] Many ancient high-Mg lavas, their <olivine> compositions and <spinifex textures> indicate large degrees of melting and high parental temperatures. Their abundance in Archean terrains and rarity in the recent record are consistent with a hotter past. However, a hot <mantle plume>, dissolved <water>, unusual source composition or crystal accumulation can change the interpretation. A komatiite temperature is not automatically the ambient mantle temperature, and <spinifex texture> alone is not a calibrated thermometer.
\b[Melting residues and crustal products provide independent checks.] Depleted <peridotite> <mantle xenoliths>, preserved mineral chemistry and compatible-element depletion constrain former melt fractions. More extensive melting can produce thicker mafic <crust> and more refractory residual <mantle>; these are predictions to compare with preserved rock packages and seismic or petrological constraints on ancient <lithosphere>. <Metamorphic facies> and pressure–temperature paths provide contextual evidence about geothermal regimes, but tectonic burial, decompression and preservation can mimic temporal changes. They do not directly measure $T_p$.
The most persuasive inference is therefore \b[agreement between dated melt thermometry, melting residues and their predicted crustal consequences], while separating source fertility, volatile content, <mantle plume> anomalies, alteration and selective preservation. Those controls explain why hotter ancient melting is better established than one exact global cooling curve.
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