B737-300 FLT CREW HAS AN APU FIRE WARNING DURING CLB TO ALT; DECLARES AN EMER AND DIVERTS TO DEP ARPT.

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I SHUT THE APU DOWN AT 3 1/2 MINS AFTER PUTTING THE ENG GENERATORS ON LINE. TAXI; TKOF AND CLBOUT WERE ALL NORMAL (CAPT FLYING). AT ABOUT FL250; MY HEADSET STARTED SHORTING OUT (I COULD HEAR BUT NOT TALK) AND I LOST THE ABILITY TO USE MY HEADSET MIKE. MY ONLY WAY TO TALK TO ATC OR OUTSIDE THE COCKPIT WAS THE HAND MIKE. ABOUT THIS TIME WE STARTED THROUGH FL350 AND THE FIRE WARNING BELL SOUNDED. THE LIGHT FROM THE SUN BLOCKED THE ENG AND APU LIGHTS FROM BEING SEEN VERY WELL; SO I HAD TO COVER THE LIGHTS TO MAKE SURE WHICH ONE IT WAS. ONCE I SAW THE APU LIGHT ILLUMINATED; I SILENCED THE BELL. I ASKED FO TO PULL OUT THE APU FIRE WARNING LIGHT QRH CHKLIST; WHICH HE WAS ALREADY DOING ANYWAYS. WE ACCOMPLISHED THIS CHKLIST IN ABOUT 10 SECONDS (2 ITEMS ON IT). THE LIGHT WENT OUT AND I LEVELED THE ACFT OFF AT ABOUT FL355. I ALSO STARTED BACK DOWN SLOWLY AND TOLD FO TO DECLARE AN EMER FOR POSSIBLE FIRE IN THE APU. WE RETURNED TO LAND. WE ASKED ATC TO HAVE CFR WAITING FOR US. WE WERE REQUIRED TO CHANGE FREQS SEVERAL TIMES AND EVERY TIME WE CHANGED; THE NEW CTLR ASKED US THE SAME QUESTIONS! HOW MANY SOULS ON BOARD; AND FUEL IN HOURS AND MINS? WHEN WE MADE OUR 180 DEG TURN BACK. WE WERE ACCOMPLISHING SO MANY THINGS AT THIS TIME WITH FLYING THE ACFT FIRST OF COURSE AND THEN GETTING THE WX IN ZZZ FOR THE RETURN. DISPATCH CALLS FOR THE RETURN AND NOTIFYING AND CHKING ON THE FLT ATTENDANTS; ETC. MAKING SURE THEY WERE OK AND LETTING THEM KNOW WHAT WE WERE DOING. WHEN I WAS TALKING TO THE 'A' FLT ATTENDANT HE TOLD ME BOTH THE 'B' AND 'C' FLT ATTENDANTS WERE LIGHTHEADED AND DIZZY. I ASKED HIM IF THERE WAS EXCESSIVE HEAT FROM THE BACK GALLEY AREA AND/OR SMOKE. HE SAID NO; NOT AT THIS TIME. IT SMELLED FUNNY BACK THERE. I REACHED UP AND SHUT OFF THE GALLEY PWR SWITCH IN THE COCKPIT. MY MIKE NOT WORKING JUST ADDED TO THE WORKLOAD. FO MADE MANY OF THE OUTSIDE COMS WHILE I WAS FLYING. I WAS SURE HE WAS BECOMING TASK SATURATED. I DID MAKE THE PA TO THE PAX! I TOLD THEM ONLY THAT WE HAD A LIGHT COME ON IN THE COCKPIT THAT REQUIRED US TO RETURN TO THE ARPT. I ALSO TOLD THE PAX THAT WE WOULD BE ON THE GND SHORTLY AND SORRY FOR ANY INCONVENIENCE. WE LANDED ON RWY 29 AT ABOUT 90000 LBS. I STOPPED WHERE THE FIRE TRUCK ON TXWY W COULD PULL UP BEHIND US AND CHK THE TAIL SECTION. IT ALSO GAVE US A PLACE TO SEND THE PAX IN THE EVENT OF AN EVAC.