MD83 flight crew reported cargo compartment fire warning climbing through FL200. An emergency was declared and flight returned to departure airport where warning was determined to be false.

Narrative

Departed; when approximately 40 miles south climbing through FL200 (for FL230) received cargo fire warning alert - aural and annunciated. Leveled at FL210; declared emergency as Captain (pilot not flying) carried out checklist procedures and alerted flight attendants. With continued cargo fire alert; immediately headed for our departure airport and was given continual clearance for landing on Runway XXR; opposite of current runways in use. As the Captain continued to communicate with flight attendants we set up for an overweight landing (134;000 LBS) on Runway XXR with the intention of meeting the ARFF at high speed - which we did. The ARFF reacted brilliantly (as did ATC; the Captain and the flight attendants); and were finally able to confirm the cargo fire warning was a false alarm; after some time. The Captain was coordinating with the port control and flight attendants and the decision not to evacuate was a good one; in my opinion. However; we of course treated the fire alert as if the aft cargo hold fire was real. After release by the ARFF we were towed to the gate.