Pyrrhotite, Fe7S8, is a commonly occurring carrier of magnetic remanence and has a low temperature transition, the Besnus transition, involving a change in spin state. Variations of the thermodynamic, magnetic and elastic properties through this transition at ∼33 K in a natural sample of 4C pyrrhotite have been tested against a group theoretical model for coupling between order parameters relating to Fe/vacancy ordering (irrep U 1(1/2,0,1/4)) and magnetic ordering (irreps m[Formula: see text] and m[Formula: see text]). Magnetoelastic coupling is weak but the pre-existing microstructure of ferroelastic and magnetic domains, that develop as a consequence of Fe/vacancy and ferrimagnetic ordering during slow cooling in nature (P63/mmc → C2'/c'), causes subtle changes in the low temperature transition (C2'/c' → P [Formula: see text]). The Besnus transition involves a rotation of magnetic moments out of the a-c plane of the monoclinic structure, but it appears that the transition temperature might vary locally according to whether it is taking place within the pre-existing domain walls or in the domains that they separate. Evidence of metamagnetic transitions suggests that the magnetic field-temperature phase diagram will display some interesting diversity. Low temperature magnetic transitions in minerals of importance to the palaeomagnetism community have been used to identify the presence of magnetite and haematite in rocks and the Besnus transition is diagnostic of the existence of pyrrhotite, Fe7S8.