The magnetic stability of superconductor strands and cables is a key issue in the successful building and operation of high-field accelerator magnets. In this paper, we report the study of a state-of-the-art 0.7 mm Nb3Sn restacked-rod-process strand manufactured by Oxford Instrument Superconductor Technology. This conductor will be used in Rutherford cable for a 15-TNb3Sn dipole demonstrator being built at Fermi National Accelerator Laboratory. Particularly, this study focuses on the impact of varying heat treatment conditions on the stability of the strand. Both the stability against internal flux jumps and external thermal perturbations are studied.