Melting in the mantle has been attributed to thermal feedback associated with the temperature dependence of viscosity during deformation (H. R. Shaw, 1969, J. of Petrol.). Visco-elastic heating has been explored in various geodynamics studies. In particular, Branlund et al. (2000, EPSL) found that a non-linear decrease of thermal diffusivity (D) with temperature (T) would enhance shear zone thinning and speed-up instabilities. Their result suggests that thermal feedback enhances melting in the uppermost mantle, without viscous heating, if considerable non-linearities exist in D(T) at the onset of melting. In fact, extreme non-linearities are indicated by theory and measurements. (1) Measurements of D of volcanic olivine-melilitite (Buettner et al. 1998, J. Volc. Geotherm. Res.) show large non-linearities in D(T) due to pre-melting effects, and a discontinuous decrease in D upon melting. This behavior should be general, because increasing disorder reduces D (e.g., Giesting & Hofmeister, 2002, Phys.Rev. B). (2) Our laser-flash measurements of various glasses show that D depends non-linearly on T. Melts will behave similarly. To quantify the functionality we are applying the melting experiments of Buettner et al. to Icelandic lavas and other relevant materials. In our runaway model, melting under ridges or hotspots does not define a magma chamber, but rather occurs on grain boundaries of the solid phases. A small amount of melting decreases D precipitously and raises the temperature which induces more melting. This phenomena is confined to low pressures (as D increases with P) and T below 2,000 K, wherein radiative effects are unimportant, and can occur in a low temperature gradient. Thus, production of magmas at hot spots need not require a deep, lower-mantle plume.