A seal system has: a first member; a seal carried by the first member and having a seal face; and a second member rotatable relative to the first member about an axis. The second member has: a seat, the seat having a seat face in sliding sealing engagement with the seal face; and a circumferential array of passageway legs. The second member further has an annular channel axially spaced from the seat face, the passageway legs connected to the annular channel.