MD-83
Flight Crew Air Transport Pilot (ATP)
Distraction; Situational Awareness; Troubleshooting
Aircraft Equipment Problem Critical
Flight Crew Returned To Departure Airport; Flight Crew Landed in Emergency Condition; General Declared Emergency
Aircraft
My takeoff; reduced thrust power.  This is our third flight of the day with this aircraft.  After gear up and just prior to 1;000 feet; we get a fire warning on the left engine.  The First Officer silences the bell and we note that the engine indications look normal.  The First Officer declares an emergency and Tower asks us to switch to Departure Control; which we do.  The First Officer then gets out the Engine Fire/Damage/Separation Checklist.  After level off; the fire light went out as soon as the throttle was pulled to idle.  There were no indications of severe engine damage/separation.  In fact; the fire light never came back on and the left engine indications were normal throughout the flight.  We make a climb to 3;000 feet and followed ATC headings for a return to land on XXR.  On downwind; I gave control of the aircraft to my First Officer so I could brief my flight attendants and make a PA to the passengers.  On crosswind with the gear down; I took back control of the aircraft.  I kept the left engine running during the flight and flew a visual approach to XXR with an uneventful landing.  Approach and landing were made with the left engine at idle.  After landing; I stopped straight ahead on the runway and immediately made a PA telling the passengers to remain seated while the First Officer started radio contact with the Fire Chief.  The Fire Chief made a complete circular inspection of our aircraft; including a thermal scan of the left engine.  He stated that all looked normal and we requested taxi to our gate.  We shut down the left engine during taxi to the gate.  I would like to add that ATC was very helpful and seemed to anticipate what we wanted/needed.
[This Report contains no additional information.]
A MD-83 Left Engine Fire Warning alerted at 1;000 feet after takeoff but extinguished when thrust was reduced; so an emergency was declared and the flight returned to the departure airport with engine running where a thermal scan detected no abnormal heat.