A SF340 RETURNED TO LAND WHEN THEY WERE UNABLE TO CONTROL HIGH DUCT HEAT CAUSING A HIGH CABIN TEMP AND DETECTED AN ABNORMAL ENG ITT TEMP DIFFERENTIAL.

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AFTER PUSHING BACK FROM THE GATE AT ZZZ FOR DEP TO ZZZ1 AND BOTH ENGS RUNNING; WITH THE #2 ENG IN CROSSBLEED; CREW RECEIVED MASTER CAUTION WITH L DUCT OVERHEAT TEMP LIGHT. L AUTO TEMP SELECTOR WAS ALL THE WAY DOWN TO COLD AND WAS THE PROBABLE CAUSE OF THE OVERTEMP. CREW RAN THE QRH PROCS FOR THE LIGHT AND THE LIGHT EXTINGUISHED. WHILE CLBING OUT OF ZZZ ARPT AFTER DEP; CABIN CREW CONTACTED THE FLT CREW SAYING THE CABIN WAS EXTREMELY HOT. CHKING THE GAUGE; WE HAD HOT AIR BLOWING FROM THE L ACM AND THE DUCT TEMP WAS AROUND 75 DEGS. I CALLED FOR THE QRH AGAIN; AND THE PROC WAS BEING FOLLOWED FOR THE OVERTEMP. AT A SAFE ALT; I CONTACTED MAINT TO ADVISE THEM OF THE PROB. WE ELECTED TO TRY MANUAL MODE AS PRESCRIBED IN THE QRH FOR HOT CABIN. SHORTLY AFTER; I NOTICED A DRAMATIC DIFFERENCE IN ITT TEMPS. WE DECIDED TO DISCONTINUE THE CABIN TEMP PROB AND PROCEEDED TO THE ITT SHIFT QRH. THE QRH EVENTUALLY DIRECTED US TO CALL MAINT. THE ITT SHIFT WAS A 65 DEG RAISE ON THE R ENG; THE OPPOSITE SIDE FROM THE ACM PROB. AFTER CONFERRING WITH MAINT AND DISPATCH; WE ELECTED TO RETURN TO ZZZ. WE CONTACTED THE FLT ATTENDANT AND TOLD HER WE WERE RETURNING TO ZZZ FOR A HOT ENG; NO NEED FOR ANY SPECIAL CABIN CONSIDERATIONS; AND THAT WE WOULD WORK ON THE TEMP. WE ALSO MADE AN ANNOUNCEMENT TO THE PAX SAYING WE WERE RETURNING FOR A PRECAUTION. ATC ASKED IF WE NEEDED PRIORITY AND WE SAID NO; BUT WE WOULD LIKE THE MOST DIRECT RTE. WE THEN XFERRED CTLS BACK AND THE FO WAS GOING TO DO THE DSCNT CHKLIST AND CONTACT DISPATCH FOR LNDG NUMBERS IN ZZZ. MEANWHILE; ATC DIRECTED US TO TURN W AND SLOW OUR AIRSPD. AT THAT TIME; I ELECTED TO DECLARE AN EMER AND REQUEST PRIORITY TO GET IN ASAP; DUE TO THE UNKNOWN CAUSE OF THE MULTIPLE PROBS. WE WERE LESS THAN 10 MINS FROM LNDG. AFTER GETTING THE NEW LNDG NUMBERS FOR ZZZ; THE FO AGAIN CONSULTED THE QRH FOR THE HOT CABIN. WE THEN FOLLOWED THE REST OF THE PROCS WHICH DIRECTED US TO TURN OFF THE L BLEED AND HP VALVES. THE HOT AIR FROM THE L ACM THEN DISCONTINUED AND TEMP STOPPED RISING. WE THEN FLEW A NORMAL VISUAL APCH TO RWY 30R AT ZZZ AND LANDED AND TAXIED IN WITHOUT FURTHER INCIDENT.