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An attemporator controls steam temperature while a desuperheater removes whatever superheat there is in steam and reduces the temperature to a point at or nearly at saturation temperature.
Attemporators are generally found in and/or associated with boiler steam, in zones where too high of a temperature affects something down stream of that point. An attemporator might be used between superheater zones in a multi-zone superheater boiler or in a re-heater zone to control reheater outlet temperture.
Desuperheaters are generally found in steam lines away from the boiler or boiler outlet piping where there is a downstream use for saturated steam.
Desuperheated steam is generally controlled to 5F - 10F above saturation (depending on the sophistication of the device) because if the temperature is controlled at saturation when it goes below the saturation line into the moisture region, the temperature controller cannot detect this.