Experimental data have been obtained for viscosities of tholeiite melts at temperatures from 1300 to 1120 °Cat 1 atm, using a concentric cylinder viscometer. The apparent viscosity increases more than two orders of magnitude between 1200 and 1120 °C (0–25 per cent crystallization) for shear rates of about 10 sec^-1 and even more for lower shear rates. Non-Newtonian behaviour of ‘pseudo-plastic type’ becomes extremely pronounced at temperatures below about 1130 °C. At these temperatures, differences of less than 5 °C can produce changes in apparent viscosity amounting to orders of magnitude. These observations have led to the conclusion that the heat of deformation must itself influence rheological behaviour in the melting range. An equation for thermal energy balances and their rates of change is constructed and placed in a non-dimensional form that has been given published solutions by I. J. Gruntfest (1963) relating the shear stress, rate of strain, and temperature through the temperature dependence of viscosity. The results show that in an adiabatic system the heating rate increases with time so that the temperature eventually runs out of bounds, a process termed ‘thermal feedback’ by Gruntfest. A hypothesis of shear melting is derived on the basis of a simplified viscosity function extrapolated to the solidus temperature. The hypothesis is applied to magma generation in the earth on the basis of dimensional arguments. It is also suggested that thermal instabilities give rise to a sort of viscous failure responsible for deep-focus earthquakes, and that the two phenomena have the same cause relating ultimately to a gravitational energy source.