PRIMELT2.XLS software is introduced for calculating primary magma composition and mantle potential temperature (TP) from an observed lava composition. It is an upgrade over a previous version in that it includes garnet peridotite melting and it detects complexities that can lead to overestimates in TP by >100°C. These are variations in source lithology, source volatile content, source oxidation state, and clinopyroxene fractionation. Nevertheless, application of PRIMELT2.XLS to lavas from a wide range of oceanic islands reveals no evidence that volatile-enrichment and source fertility are sufficient to produce them. All are associated with thermal anomalies, and this appears to be a prerequisite for their formation. For the ocean islands considered in this work, TP maxima are typically ~1450–1500°C in the Atlantic and 1500–1600°C in the Pacific, substantially greater than ~1350°C for ambient mantle. Lavas from the Galápagos Islands and Hawaii record in their geochemistry high TP maxima and large ranges in both TP and melt fraction over short horizontal distances, a result that is predicted by the mantle plume model