A B737-300 IN CRUISE AT FL310 DECLARED AN EMER DUE TO APU FIRE WARNING. APU PREVIOUSLY DEFERRED INOP.

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DURING FLT PLANNING; WE OBSERVED APU WAS DEFERRED INOP DUE TO NEGATIVE BLEED AIR. WE READ OPS PLACARD AND DISCUSSED COURSE OF ACTION FOR INOP APU. WE ARRIVED AT ACFT AT XA45 AND WERE MET BY A TECHNICIAN WHO BRIEFED US THAT APU WAS INOP; BUT DUE TO FAILURE OF FIRE TESTING SYS; NOT BLEED AIR. TECHNICIAN WAS VERY PLEASANT AND WE THANKED HIM FOR HIS EFFORTS. DISPATCH SENT A NEW FLT PLAN BASED ON NEW MEL ITEM AND MAINT GENERATED A NEW MAINT RELEASE. WE READ OPS PLACARD. REMAINDER OF DEP SEQUENCE WAS NORMAL. AT APPROX XC10; AT FL310; ABEAM ZZZ ARPT; WE PREPARING TO DSND INTO ZZZ2; THE APU FIRE WARNING SYS ACTIVATED. WE ACCOMPLISHED EMER QRH CHKLIST AND FLT MANUAL REF ITEMS. AN EMER WAS DECLARED WITH ATC; DISPATCH NOTIFIED VIA ACARS; FLT ATTENDANTS BRIEFED ON CABIN ADVISORY AND A PA ANNOUNCEMENT WAS MADE TO PAX. WE BELIEVED THAT THE WARNING WAS FALSE DUE TO THE FACT THAT: 1) APU HAD NEVER BEEN OPERATED; AND 2) MAINT HAD WORKED ON SYS THE NIGHT BEFORE. HOWEVER; ALL APPROPRIATE SOP ITEMS WERE ACCOMPLISHED FOR APU INFLT FIRE. WE DETERMINED THAT ZZZ2 WAS NEAREST SUITABLE ARPT. UNEVENTFUL APCH AND LNDG. WE ASKED ZZZ2 FIRE DEPT TO SCAN TAIL AREA AFTER LNDG FOR ANY EVIDENCE OF FIRE. THEY RESPONDED THAT THERE WAS NO FIRE. WE TAXIED TO GATE.