B737-500 CREW HAD AN APU FIRE WARNING AFTER BEGINNING THE APU START SEQUENCE IN ATL CLASS B AIRSPACE.

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DURING LNDG PHASE FOR ATL; APPROX 20 MI OUT; SELECTED APU SWITCH TO 'ON' POS. INITIALLY SET UP TO LAND ON RWY 26R IN NIGHT VMC. PRIOR TO APU ATTAINING PROPER OPERATING SPD; APU FIRE WARNING LIGHT; BELL; AND MASTER CAUTION ILLUMINATED. SILENCED THE BELL; CALLED FOR APU FIRE CHKLIST; AND DECLARED AN EMER. REQUESTED FIRE TRUCKS TO BE STANDING BY. WHILE CHKLIST WAS BEING ACCOMPLISHED; ATL APCH OFFERED RWY 26L TO EXPEDITE OUR ARR. WE ACCEPTED AND FO REACCOMPLISH APCH CHKLIST FOR NEW RWY. JUMPSEATING PLT; AT MY REQUEST; CONTACTED #1 FLT ATTENDANT TO INQUIRE IF THEY SMELLED ANYTHING UNUSUAL. THEY SAID THEY SMELLED A BURNING SMELL BUT NO VISIBLE SMOKE. AFTER LNDG; WE CLRED THE RWY AND I REQUESTED THAT THE FIRE CREW INSPECT THE APU/TAIL SECTION OF THE ACFT. WHILE INSPECTION WAS UNDER WAY; I CONTACTED FLT ATTENDANTS ON INTERPHONE TO INQUIRE ONE MORE TIME ABOUT CONDITIONS INSIDE ACFT. OTHER THAN FAINT SMELL; NOTHING ABNORMAL RPTED. FIRE CREW THEN RPTED NO VISIBLE FIRE OR SIGNS OF DAMAGE. CONTINUED TO TAXI TO GATE WITH FIRE CREW FOLLOWING US UNTIL WE SHUT DOWN AT THE GATE. DURING TAXI IN; INFORMED OPS AND REQUESTED MAINT MEET THE ACFT. MADE A LOGBOOK WRITE-UP. THEN WENT DOWN TO OPS AND CONTACTED DUTY DIRECTOR INFORMING HIM OF THE SIT. NEXT CONTACTED UNION SAFETY OFFICER.