GLF2 CREW HAD HIGH FUEL TEMP WHICH RESULTED IN AN INFLT ENG SHUTDOWN IN ZFW CLASS A AIRSPACE.

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ACFT DEPARTED DAL APPROX XA15 FOR HIGH ALT FLT ON IFR FLT PLAN. DURING CLB AT ABOUT FL280; PNF/CAPT NOTICED THE SINGULAR ENG FUEL TEMP GAUGE WAS SOLIDLY IN THE YELLOW ARC; AND SLOWLY GETTING HOTTER. WE HAD BEEN CLRED TO FL410 WHEN I INSTRUCTED THE PF/COPLT TO ASK CTR FOR FL350 WHILE I CHKED THE AFM AND THE SIMUFLITE CHKLIST. THE AFM STATES THE FUEL TEMP IS ALLOWED IN THE YELLOW ARC FOR 15 MINS -- WITH NO OTHER DIRECTIVES. THE SIMUFLITE CHKLIST DOES NOT ADDRESS THIS MALFUNCTION. I REQUESTED ZFW TO RTE US BACK TO DALLAS AND ASSIGN US A LOWER ALT. WE WERE CLRED DIRECTLY TO FINGR INTXN AND FL240 AND THE REMAINDER OF THE FINGR 3 STAR. WE MADE A NORMAL DSCNT AS PER THE STAR. WX WAS VFR; DAYLIGHT; LIGHT TFC. ALL OTHER ACFT SYS WERE NORMAL. DURING THE DSCNT WE THROTTLED BACK THE AFFECTED ENG TO FLT IDLE; BUT THE GAUGE MOVED TO THE RED LINE AND DID NOT SHOW ANY SIGNS OF DECREASING. I DIRECTED THE PF TO SHUT DOWN THE ENG AND WE CONTINUED THE DSCNT VIA ATC'S INSTRUCTIONS. THE ACFT HAD NO OTHER OPDEVS; OR REQUIRED ANY OTHER CONSIDERATIONS. WHEN ASKED INITIALLY BY CTR WHAT OUR DIFFICULTIES WERE; I TOLD THEM WE WERE OPERATING WITH REDUCED PWR FROM #1 ENG AND DID NOT REQUIRE ANY SPECIAL HANDLING. THE RETURN ROUTING TOOK US DIRECTLY TO LOVE FIELD WITH A NORMAL LNDG AND TAXI IN. I RPTED WHAT HAPPENED TO THE AVIATION MGR AND 5 MINS LATER WE WERE TAXIING OUT IN A DIFFERENT GII THAT HAD BEEN PREPPED AND PREFLTED BY OUR DEPT PERSONNEL. A MALFUNCTION OF THIS NATURE IS VERY RARE. THE ENG FUEL TEMP CONTROLLER IS AFFIXED TO THE ENG AND SUPPLIED WITH MAIN AIR DUCT HOT AIR. THERE IS NO COCKPIT CTL OF ITS FUNCTION. OTHER THAN OUR ATTEMPT TO REDUCE THE GAUGE INDICATION BY REDUCING PWR AND THEN SHUTTING DOWN THE ENG; NO OTHER PROCS ARE POSSIBLE. NUMEROUS TIMES WE'VE BEEN TOLD DURING RECURRENT TRAINING THAT THIS GAUGE HAS A 15 MIN LIMITATION IN THE YELLOW ARC AND REQUIRES A WHOLE ENG FUEL SYS OVERHAUL IF THE RED LINE WAS REACHED. 3 DAYS LATER THIS ENG IS NOW COMING OFF THE AIRFRAME AS PER GULFSTREAM MAINT PROCS. THE MAINT MANUALS ALLOW A MORE GENEROUS TIME LIMITATION; BUT I COULD NOT POSITIVELY STATE HOW LONG THE ENG HAD OPERATED ABOVE NORMAL BEFORE I NOTICED IT. THIS GAUGE IS LOCATED IN THE GII IN AN OBSCURE LOCATION ABOVE THE COPLT'S POS R KNEE; AND IS NOT CONNECTED TO THE ANNUNCIATOR SYS. THE PLT CANNOT SEE THIS GAUGE FROM HIS POS; AND THIS GAUGE IS NOT A CHKLIST ITEM. WITH RESPECT TO THIS FLT; I AM CERTAIN THAT WE OPERATED WITHIN THE SCOPE OF FAR PART 91 WHILE MAKING A NORMAL DSCNT AND RETURN TO LNDG. THERE IS NO OTHER WAY TO ASCERTAIN THE ACCURACY OF THIS GAUGE. YOU HAVE TO HONOR WHAT IT IS TELLING YOU. FURTHER OP OF THIS ENG ONCE IT REACHED THE LINE WOULD HAVE COMPROMISED THE ENG CORE AND POSSIBLY LEAD TO TOTAL FAILURE. AT NO TIME DURING THE RETURN TO LNDG DID I FEEL THE SKIN WAS IN DANGER OR REQUIRED ANY EMER DECLARATION. AT THE TIME OF THIS FLT; THE FUEL TEMP GAUGE IS NOT LISTED AS A CHKLIST ITEM. I AM CHANGING THAT NOW TO BE INCLUDED IN 'BEFORE TKOF' AND DURING 'CLB' TO BE INCORPORATED IN MY CHK. RIGHT NOW CHKING THIS GAUGE IS HIT OR MISS; DEPENDING ON THE SCAN HABITS OR PATTERNS OF EACH CREW MEMBER. I'M GLAD I DID NOT HAVE TO DEAL WITH THIS AT 30 DEGS W OR OVER THE AMAZON AT NIGHT!