MD80 CREW HAD THE TAIL COMPARTMENT TEMP HIGH LIGHT ILLUMINATE DEPARTING LAS.

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WE HAD A GREAT DEAL OF TROUBLE DEALING WITH LAS GND OPS AND KEEPING OUR ACFT COOL. WE RAN THE APU FOR OVER AN HR IN 106 DEG HEAT DUE TO A VERY HOT AIRPLANE AND VERY LITTLE HELP IN LAS. ON ROTATION WE GOT A TAIL COMP HIGH TEMP LIGHT; WHICH DUE TO HOT WX AND A SLOW CLB; STAYED ON FOR OVER 4 MINS. THE LIGHT WENT OUT WHEN WE LEVELED OFF. I DECIDED TO RETURN TO LAND AND WAS CONVINCED THIS WAS DUE TO AN OVERHEATED APU. WE DECLARED AN EMER FOR AN OVERWEIGHT LNDG. WE TOOK A LONG DOWNWIND BEFORE TURNING FINAL BOTH TO COMPLETE CHKLISTS; AND BURN DOWN A LITTLE; THEN PROCEEDED TO AN UNEVENTFUL LNDG AT 138200 LBS. ALTHOUGH I WAS POSITIVE OF THE PROB BEING CAUSED BY AN OVERHEATED APU; IT HAD BEEN BORDERING BTWN THE YELLOW AND RED ARC WHILE AT THE GATE; THUS MY PROBS WITH LAS GND OPS. I HAVE BEEN ON THE ACFT LONG ENOUGH THAT I DECIDED TO LAND ANYHOW. TURNS OUT THE PROB WAS A BLOWN DUCT ON THE L PACK. ALTHOUGH I UNDERSTAND THE CAPT'S DISCRETION TO CONTINUE BULLET IN OUR PROCS; I WOULD HIGHLY ENCOURAGE THAT BULLET TO BE INCLUDING A STATEMENT ABOUT LONG FLTS VERSUS SHORT. I HAVE HAD 4 OF THESE IN MY 11 PLUS YEARS ON THIS ACFT; AND I HAVE HAD TWO BLOWN DUCTS; PLUS OTHER MECHANICAL PROBS. THE MECH WE SPOKE WITH SAID THIS COULD HAVE POTENTIALLY CAUSED A FIRE; OR AT THE VERY LEAST; PRESSURIZATION ISSUES AT ALT.