Necking of the lithosphere involves complex nonlinear thermal-mechanical feedback mechanisms in an elasto-viscoplastic plate. The mode of extension of such plates relies on the mechanical properties of the upper part of the mantle and on the nucleation of ductile faults within the lithosphere. Our numerical model addresses the key problem of controls of ductile failure of the strongest part in the lithosphere. It is found that a small heterogeneity within this strong part can nucleate quasi-adiabatic shear bands. These develop spasmodically with time as finite amplitude instabilities with increasing temporal and length scales. The largest shear zone takes about 100,000 years to propagate through the entire lithosphere and can lead to a thermal instability for an ambient mantle temperature larger than 900 K. In our numerical model, thermal runaway occurs when the plate is severed. The temperature rise of the thermal instability is a function of the creep law exponent n and can be quenched for a lower n and smaller activation energy. The model is applicable to the problem of onset of continental break-up and holds the key to ductile instabilities in the Earth's lithosphere. The changing hot surface temperature on Venus might also have precipitated lithospheric instabilities in the past.