, a HS 748, departed Whitehorse (YXY) for Dawson and a short time after takeoff, the crew received a fire warning bell for the left engine. They followed the fire drill checklist and discharged the fire bottles, but the indication would not go off. They elected to return to YXY and the fire warning light went off just as the a/c was landing on Runway 13R. No other a/c were inconvenienced by the incident. Maintenance found no evidence of fire, but found that the fire control relay unit was intermittent. They replaced the unit and the base upon which the unit sits. They also found that the supercharger duct sleeve was worn, allowing hot air to vent near the sensor of the fire control unit, which may have contributed to the alarm being activated. The repairs have been done and the a/c has been released to service. OPI - Maintenance and Manufacturing UPDATE M. & M. reported that no further investigation is required. An SDR has been requested from the company.