Metallic/intermetallic materials with BCC structures hold an intrinsic instability due to phonon softening along [110] direction, causing BCC to lower-symmetry phases transformation when the BCC structures are thermally or mechanically stressed. Fe₅₀Rh₅₀ binary system is one of the exceptional BCC structures (ordered-B2) that has not been yet showing such transformation upon application of thermal stress, although mechanical deformation results in B2 to disordered FCC (γ) and L1₀ phases transformation. Here, a comprehensive transmission electron microscopy (TEM) study is conducted on thermally-stressed samples of Fe₅₀Rh₅₀ induced by quenching in water and liquid nitrogen from 1150 °C and 1250 °C. We demonstrated that samples quenched from 1150 °C into water and liquid nitrogen show the presence of 1/4{110} and 1/2{110} satellite reflections, the latter of which is expected from phonon dispersion curves obtained by density functional theory calculation. Therefore, it is proposed that Fe₅₀Rh₅₀ maintains the B2 structure that is in premartensite state. Once Fe₅₀Rh₅₀ is quenched from 1250 °C into liquid nitrogen, formation of two short-range ordered tetragonal phases with various c/a ratios (∼1.15 and 1.4) is observed in line with phases formed from mechanically deformed (30 %) sample. According to our observations, an accurate atomistic shear model ({110}〈11¯0〉) is presented that describes the martensitic transformation of B2 to these tetragonal phases.