AN SF340B FLT CREW GOT A 'BLEED CLOSED' LIGHT AND WERE UNABLE TO CONTROL DUCT TEMP. THEY FOLLOWED QRC THAT RESULTED IN INFLT ENG SHUTDOWN.

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WE RECEIVED A R 'BLEED CLOSED' LIGHT ILLUMINATION. WE WENT TO THE QRH AND RESET IT (BLEED FAULT CHKLIST). WE NOTED THAT THE L DUCT TEMP INDICATION WAS MAINTAINING 25 DEGS C; NORMAL FOR THE CRUISE ALT OF 17000 FT. THE FLT ATTENDANT CALLED ABOUT THIS TIME AND NOTIFIED US THE TEMP IN THE CABIN WAS WARM; SO WE SELECTED A COLD SETTING ON THE AUTO TEMP CTL AND NOTHING CHANGED. THE R BLEED FAILED AGAIN (R BLEED CLOSED LIGHT ILLUMINATED). WE RESET IT. ACCORDING TO THE QRH 2 ATTEMPTS ARE ALLOWED. WE ALSO SWITCHED FROM AUTO TO MANUAL TEMP CTL AND HELD SWITCHES TO FULL COLD WITH NO CHANGE. L DUCT TEMP WAS INDICATING MAINTAINING 25 DEGS C. JUST PRIOR TO DSCNT; R BLEED VALVE CLOSED AGAIN. WE DID NOT RESET AND TEMP ROSE TO ABOUT 30 DEGS C; BUT SINCE THE PWR WAS BROUGHT BACK A LITTLE; I THOUGHT IT WAS NORMAL. I CONTACTED MAINT CTL NOTIFYING THEM OF THE BLEED FAILURE AND ASKED THEM IF THERE WAS ANY OTHER CONCERNS AND TOLD THEM THAT L DUCT TEMP WAS MAINTAINING 25 DEGS C AND WOULD NOT COME DOWN IN MANUAL OR AUTO. AT LEVELOFF AT 8000 FT; AS PWR WAS INCREASED; L DUCT TEMP ROSE RAPIDLY ABOVE 40 DEGS C. I TRIED TO MANUALLY SELECT COLD BUT TEMP INDICATION CONTINUED TO RISE. QRH SAYS TO 'CONSIDER ENG SHUTDOWN' IF UNABLE TO CTL TEMP. I DISCUSSED WITH MY FO AND WE ELECTED TO COMPLY WITH THE QRH. I COMPLETED THE ENG SHUTDOWN. AS PWR WAS INCREASED ON THE L ENG FOR THE ENG SHUTDOWN; TEMP IN THE L DUCT WAS WELL ABOVE 50 DEGS C. WHEN R ENG WAS SHUT DOWN; L DUCT TEMP FELL RAPIDLY TO 15 DEGS C AND FLUCTUATED BTWN 15 DEGS C AND 25 DEGS C; DEPENDING ON THE PWR SETTING; VERY NORMAL. ALSO; I CYCLED MANUAL TEMP CTL BRIEFLY AND L DUCT TEMP INDICATION FLUCTUATED NORMALLY. PRIOR TO THE SHUTDOWN OF THE R ENG; I WAS UNABLE TO GET ANY RESPONSE WITH THE TEMP CTL. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE REPORTER STATED THEY WERE WITHIN 11 MILES OF DESTINATION; SO THEY CONTINUED TO THEIR SCHEDULED DESTINATION. NO EMERGENCY WAS DECLARED; SINCE THE TOWER TOLD THEM CFR EQUIPMENT WAS ALREADY STANDING BY.