Time evolution of temperature distributions of selected tracers with redshift. As in Figure 12 (right panel), but splitting by parent categories (Section 2.2). Each panel shows tracers of only one origin category. Top left: Tracers outside of all halos, i.e. in the IGM (unbound). Top right: Tracers in other halos, i.e. not within the main progenitor of the primary cluster halo (other halo). Bottom left: Tracers in the primary cluster halo – that is, the central galaxy or the diffuse ICM – or its progenitors (primary halo). Bottom right: Tracers in satellites of the primary cluster halo (satellites). The particles in the primary halo contribute to redshift z = 0 cool gas via in situ cooling of virialized hot gas, while satellites and other halos contribute primarily pre-cooled gas to clusters.