Temperature controlled in situ wax purification

A hydrocarbon wax product from a HCS slurry comprising liquid synthesis product and catalyst particles is purified by circulating the slurry from a synthesis zone with a first temperature through a treatment zone with a second temperature in which a hydrogen-containing treatment gas contacts the slurry. The gas treatment removes impurities from the hydrocarbon wax product and also removes catalyst de-activating species which may be present in the slurry. Purified wax product is separated and removed from the treated slurry via wax withdrawal means. This avoids or minimizes the need for further treating the wax product. Remaining treated slurry may be returned to the synthesis zone.