B727 CREW HAD AN APU FIRE WARNING IN ZDV CLASS E AIRSPACE.

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DURING THE PRE TKOF FLOW; I WAS INTERRUPTED BY A QUESTION FROM THE CAPT. THE CAPT KNEW I HAD WORKED WITH FIRE FIGHTING ACFT (3 YRS) AND ASKED ABOUT A SMOKE JUMPER OTTER BEING CLRED TO TAKE OFF. I EXPLAINED WHAT SMOKE JUMPER ACFT DID. HE ASKED ABOUT THE LARGER ACFT; AND I BRIEFLY DESCRIBED WHAT TANKERS DO. AS I WAS TALKING; TWR THEN CLRED US FOR 'IMMEDIATE TKOF;' ADDING 'THE SMOKE JUMPER WILL BE TURNING OUT L AHEAD OF YOU;' AND 'YOU'LL ALSO HAVE ACFT X ON 5 MI FINAL BEHIND YOU.' THE CAPT SAID WE'D MAKE A ROLLING TKOF AND CALLED FOR 'BELOW THE LINE' (THAT PORTION OF THE BEFORE TKOF CHK; DONE WHEN TAKING THE ACTIVE). I NEVER WENT BACK TO COMPLETE MY FLOW AND LEFT THE APU RUNNING ON TKOF. CLBING THROUGH 17000 FT; THE FIRE WARNING HORN SOUNDED. THE CAPT SAID; 'WHAT'S THIS?' THE FO SAID; 'WE HAVEN'T GOT ANY LIGHTS OR INDICATIONS OF FIRE UP HERE.' I CHKED THE ENG GAUGES; THE SO PANEL; AND REACHED FOR THE HORN CUTOUT ON THE APU PANEL; AND NOTICED IMMEDIATELY I HAD LEFT THE APU ON. I TOLD THE CAPT WHAT I HAD DONE; AND ASKED IF HE WANTED ME TO 'PULL THE HANDLE AND DISCHARGE THE BOTTLE.' HE SAID YES; BUT 'GET OUT THE RED TABS AND FOLLOW THE CHKLIST.' I DID THIS. THE CAPT FILED A FLT SAFETY RPT WITH OUR FLT SAFETY DEPT AND I AM DUE TO DEBRIEF WITH THEM. I ALLOWED MY FLOW TO BE INTERRUPTED; FAILED TO GO BACK TO FINISH IT; AND DID NOT CATCH MY OMISSION WITH A CHKLIST DURING AN EXPEDITIOUS DEP.