Thermomechanical deformations of a body made of two different materials and under-going simple shearing deformations are studied with the objectives of finding out when and where adiabatic shear bands will initiate and how they will subsequently grow. Each material is modeled as strain and strain-rate hardening but thermally softening. A shear band is presumed to have formed if the introduction of a temperature perturbation centered around the common interface between the two materials results in an eventual localization of the deformation into a region of width considerably smaller than the width of the initial temperature bump. For a fixed set of material properties the effect of the applied overall strain-rate, and for a fixed applied strain-rate the effect of varying the shear modulus, thermal conductivity, and the coefficient of thermal softening of one material relative to the other have been examined. It is found that a shear band forms in the material that softens more rapidly.