We consider a system of hyperbolic-parabolic equations describing a material instability mechanism associated to the formation of shear bands at high strain-rate plastic deformations of metals. We consider the case of adiabatic shearing and derive a quantitative criterion for the onset of instability: Using ideas from the theory of relaxation systems we derive equations that describe the effective behavior of the system. The effective equation turns out to be a forward-backward parabolic equation regularized by fourth order term. Further, we study numerically the effect of thermal diffusion on the evolution of these bands. It turns out that while localization initially forms at a later stage of the deformation heat diffusion has the power hinder and even altogether suppress localization and even return the evolution to uniform deformation. (joint work with Th. Katsaounis and Th. Baxevanis, Univ. of Crete).