Abstract  We study the set of KMS states of spin systems with random interactions. This is done in the framework of operator algebras by investigating Connes and Borchers –invariants of W*–dynamical systems. In the case of KMS states exhibiting a property of invariance with respect to the spatial translations, some interesting properties emerge naturally. Such a situation covers KMS states obtained by infinite–volume limits of finite–volume Gibbs states, that is the quenched disorder. This analysis can be considered as a step towards fully understanding the very complicated structure of the set of temperature states of quantum spin glasses, and its connection with the breakdown of the symmetry for replicas.