In body-centered cubic (bcc) crystals, ${1}{2}111$ screw dislocations exhibit high intrinsic lattice friction as a consequence of their non-planar core structure, which results in a periodic energy landscape known as the Peierls potential, $U_P$. The main features determining plastic flow, including its stress and temperature dependences, can be derived directly from this potential, hence its importance. In this Letter, we use thermodynamic integration to provide a full thermodynamic extension of $U_P$ for bcc Fe. We compute the Peierls free energy path as a function of stress and temperature and show that the critical stress vanishes at 700K, supplying the qualitative elements that explain plastic behavior in the athermal limit.