Oligocene volcanics from Oatlands in Tasmania, Australia, include olivine tholeiites, alkali olivine basalts, nepheline basanites and olivine nephelinites. They have compositional characteristics that are typical of intraplate basalts worldwide. They are generally enriched in incompatible elements relative to the primitive mantle and are strongly enriched in Nb, Ta and light rare earths, but not heavy rare earths. At the same time, they have Sr and Nd isotope compositions that are similar to those in some incompatible-element-depleted mid-ocean ridge basalts (E-type MORB). Experimentally obtained mineral/melt partition coefficients for an Oatlands basanite allow the relative concentrations of incompatible elements in the volcanics to be produced by small degrees of melting (≤1%) of a source similar to the E-type MORB source of Workman and Hart (2005). However, the absolute concentrations that can be achieved in this way are much less than present in the most incompatible-element-enriched basanites and nephelinites at Oatlands. This contradiction can be explained by open-system melting under the influence of a conductive geotherm. This would have involved upwardly migrating near-solidus melts from the asthenosphere cooling along a sub-adiabatic geotherm. Cooling of the melts would have caused them to re-crystallize and accumulate in the overlying mantle, thereby enriching both the new host rocks and any residual melts in incompatible elements. This would also have increased the buoyancy of the host rocks leading to upwelling and further (decompression) melting of incompatible-element-enriched peridotite. We were able to use our partition coefficients to quantitatively model the development of incompatible-element enrichments in the Oatlands magmas by these processes. Our explanation is consistent with the characteristically scattered but widespread distributions and long time scales of intraplate volcanism in a broad variety of tectonic settings. This is because the conditions required to initiate volcanism (i. e. those of near-solidus melting of the asthenosphere) are relatively easy to produce and can therefore be caused by both near-surface tectonics and deeper mantle processes. Furthermore, the super-enrichments of incompatible elements in some intraplate volcanics can be attributed to the influence of normal geothermal gradients on melting processes. Without the very strong fractionation imposed by this combination of factors, the Oatlands volcanics would more closely resemble mid-ocean-ridge basalts.