We have studied the effects of viscous heating involving heterogeneous media which occurs in the interaction between the mantle-lithosphere-crust system with the mantle-lithosphere in delamination. High rates of viscous heating are found in corner flow regions, where the deformation rate of the flow is highest. The weak lower crust is sheared between the upper crust and the mantle-lithosphere, giving rise to a second type of viscous heating with high dissipation values several ten to hundred times the chondritic value. Greater dissipation rates are found in the shear interaction between heterogeneous media with different non-Newtonian rheologies than in the shear heating inside a single non-Newtonian or Newtonian homogeneous medium. High spatial resolution of at least 2.5 km or finer is needed to resolve the sharp variations of viscous heating near the interface of the two media. ¿ 1999 American Geophysical Union