What was found
EN-ROUTE, AT APPROX 1 HOUR INTO FLIGHT AT A CRUISE LEVEL OF 430, THE CREW HAD AN INDICATION OF A APU FIRE. THE APU WAS NOT RUNNING. THE CREW FOLLOWED THE AFM CHECKLIST & DISCHARGED THE FIRE BOTTLE & THE INDICATION REMAINED. AT THAT TIME THEY DECLARED AN EMER & DIVERTED. ONCE THEY LANDED THE FIRE DEPARTMENT MEET THE ACFT & VERIFIED THERE WAS NO FIRE OR EVIDENCE OF A FIR. TECHNICIANS WERE DISPATCHED TO THE ACFT & ALSO VERIFIED THERE WAS NO FIRE. AFTER TROUBLESHOOTING THE PROBLEM, FOUND THAT THE APU INLET FIRE TEMP SENSOR HAD A LOOSE CONNECTION.