The formation of the intermetallic 𝜎 phase (space group 𝑃⁢42/𝑚⁢𝑛⁢𝑚) has a detrimental effect on the ductility of transition-metal alloys. This theoretical study uses first-principles calculations to investigate the stability and thermodynamic properties of the WRe and WOs 𝜎 phases. Our study indicates that the 𝜎 phase becomes thermodynamically stable at its ideal composition for temperatures above 1050 K and 130 K for the WRe and WOs phases, respectively. We find that models that neglect the phonon contribution to the free energy may underestimate the amount of disorder in the 𝜎 phase at elevated temperatures. Furthermore, the 𝜎 phase becomes dynamically unstable for Re concentrations above 73 at.% Re and 53 at.% Os. For the WOs phase, the dynamic stability is sensitive to the lattice site occupation, and vibrations of the Os atoms are linked to the transformation into a dynamically stable orthorhombic phase.