The Earth's inner core is primarily composed of iron, but the stable crystalline structure of iron under core conditions still remains uncertain. The body-centered cubic (bcc) phase has been suggested as a possible candidate to explain the observed seismic complexity, but its stability at core conditions is highly disputed. In this study, we utilized thermodynamic integration techniques based on extensive first-principles molecular dynamics simulations to analyze the combining effects of high temperature and impurities on the stability of bcc structure with respect to tetragonal strain. According to our simulations, a small amount of Si/S permitted by seismological data at high temperature increases the stability of the bcc structure at high pressure, but not enough to achieve complete stability. This means the bcc-structured iron is highly unlikely to present in the Earth's inner core.