The present study employs the method of atomistic simulation to estimate the thermal stress experienced by Si/Ge and Ge/Si, ultrathin, core/shell nanowires with fixed ends. The underlying technique involves the computation of Young’s modulus and the linear coefficient of thermal expansion through separate simulations. These two material parameters are combined to obtain the thermal stress on the nanowires. In addition, the thermally induced stress is perceived in the context of buckling instability. The analysis provides a trade-off between the geometrical and operational parameters of the nanostructures. The proposed methodology can be extended to other materials and structures and helps with the prediction of the conditions under which a nanowire-based device might possibly fail due to elastic instability.