A SAAB 340B IN CLB FROM 7800 FT TO 8000 FT DECLARED AN EMER AND DIVERTED DUE TO LEFT ENG TAILPIPE HOT ANNUNCIATOR. L ENG SHUT DOWN INFLIGHT.

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WE WERE OPERATING FLT ABCD ZZZ1 - ZZZ2. I WAS THE FLYING PLT. AS I COMMENCED LEVELOFF AT 8000 FT; THE L TAILPIPE HOT ANNUNCIATOR ILLUMINATED. MY FIRST THOUGHT WAS THAT WE HAD A FALSE INDICATION. WE'D HAD SEVERAL OTHER TRANSIENT WARNING INDICATIONS DURING THE COURSE OF THE DAYS FLYING IN THIS PARTICULAR ACFT. ADDITIONALLY; IT WAS RAINING; AND THE SAAB'S TAILPIPE TEMPERATURE PROBES ARE KNOWN TO TRIGGER FALSE ALARMS WHEN WET. AFTER APPROX 20 SECONDS; THE WARNING PERSISTED; SO I COMPLETED THE ONE MEMORY ITEM FROM THE EMER CHECKLIST: 'REDUCE POWER TO 20 - 30 % TORQUE.' THE FO HAD ALREADY PULLED OUT THE CHECKLIST. THE ANNUNCIATOR REMAINED ON. IN THIS EVENT; THE CHECKLIST CALLS FOR A PRECAUTIONARY ENG SHUT DOWN. WE ACCOMPLISHED THIS; DECLARED AN EMER; AND RECEIVED VECTORS TO THE ILS 1R AT ZZZ. THE FO NOTIFIED OUR FA; THEN COMPLETED THE ONE ENG INOP DSCNT; APCH; AND LNDG CHECKS. APCH AND LNDG WERE OTHERWISE NORMAL; ALTHOUGH I FOUND FULL L RUDDER APPLICATION WAS NECESSARY DURING ROLLOUT. THE YAW DAMPER HAD DRIVEN THE RUDDER TRIM FULL R. IN HINDSIGHT; I SHOULD HAVE REQUESTED THE FO NEUTRALIZE THE TRIM JUST PRIOR TO TOUCHDOWN. OUR MECHANICS FOUND THE TAILPIPE TEMP PROBES TO BE IN POOR CONDITION. THEY REPLACED THE PROBES; AFTER WHICH WE CONDUCTED A HIGH POWER RUN UP WHICH PROVED NORMAL. IT IS UNFORTUNATE THAT NEITHER THE WARNING SYSTEM NOR THE CHECKLIST PROVIDE A SECONDARY MEANS TO DETERMINE THE VALIDITY OF THE INDICATION. THIS COULD PREVENT UNNECESSARY SHUT DOWNS. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE RPTR STATED THAT DURING THE DAY'S FLYING; SEVERAL TRANSIENT TAILPIPE 'HOT' WARNINGS WERE RECEIVED MOMENTARILY. THE RPTR SAID IT RAINED MOST OF THE DAY AND AGGRAVATED AN ALREADY BAD SITUATION WITH THE TAILPIPE 'HOT' WARNING SYSTEM. THE RPTR SAID WITH THE POWER PULLED BACK; THE LIGHT WOULD NOT GO OUT. THE RPTR STATED THE ENG WAS SHUT DOWN PER THE PROCS AND A SINGLE ENG LNDG WAS MADE UNEVENTFULLY. THE RPTR SAID ON THE GND MAINT REPLACED THE SYSTEM SENSOR PROBES; WHICH PROVED TO BE IN POOR CONDITION. CALLBACK FROM ACN 604506: THE RPTR STATED THE TAILPIPE 'HOT' ANNUNCIATOR CAME ON WITH CLB POWER; AND WHEN THE MEMORY ITEM TO PULL POWER BACK TO 30% OR 20% WAS FOLLOWED; THE ANNUNCIATOR REMAINED ON. THE RPTR SAID THIS AIRPLANE 'HOT' TAILPIPE WARNING IS AFFECTED BY RAIN AND CAN CAUSE FALSE WARNINGS. THE RPTR STATED THIS AIRPLANE IF LEFT OUTSIDE OVERNIGHT MUST HAVE TAILPIPE COVERS TO PREVENT INTERNAL LEAKAGE OF WATER.