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A data storage system includes multiple tiers of data storage accessible by multiple hosts. The multiple tiers include an upper tier having a lower access latency and a lower tier having a higher access latency. For each extent among a plurality of extents of file system objects in the data storage, the storage controller separately tracks, for each of one or more hosts that access the extent, a respective heat indicative of a frequency of access by that host. In response to an event disassociating a first host among the multiple hosts from a particular extent among the plurality of extents, the storage controller recalculates an overall heat of the particular extent while excluding a first heat of the first host for the particular extent. The storage controller migrates extents among the multiple tiers based on overall heats of the plurality of extents.