FLC OF ACR MLG ACFT EXPERIENCED A 'HOT ENG START' DURING TAXI FOR TKOF.

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APPROX AT THE INTXN OF TAXIWAY WB AND WD; I ASKED FO TO COMPLETE THE INITIAL ITEMS OF THE DELAYED START CHKLIST AND THE #2 ENG. AS WE WERE TAXIING TO THE RWY; AS THE #2 ENG WAS STARTED; MY PRIMARY ATTN WAS ON TAXIING THE ACFT AS WE APCHED THE TURN ONTO TAXIWAY WC TO THE RWY. FO RECALLED AN EGT PEAK OF APPROX 425 DEGS AT STARTER CUTOUT FOLLOWED BY THE NORMAL EGT DROP AS THE ENG ACCELERATED. AS FO WAS FINISHING THE DELAYED START (AFTER START PORTION) CHKLIST; HE SAID OR DID SOMETHING; WHICH I CANNOT SPECIFICALLY RECALL; THAT CALLED MY ATTN TO THE ENG INSTS. I NOTED N2 RPM AT 46 PERCENT AND EGT AT 520 DEGS. I IMMEDIATELY MOVED THE FUEL LEVER FOR ENG #2 TO 'OFF' TO SHUT DOWN THE ENG. I DID NOT SPECIFICALLY NOTE ENG N2 RPM STABILIZED AT NORMAL IDLE (APPROX 51-52 PERCENT). I DO NOT KNOW IF THE N2 RPM ROLLED BACK FROM THE IDLE RANGE TO 46 PERCENT WITH THE RESULTANT OVERTEMP CONDITION OR IF THE N2 RPM STAGNATED AT 46 PERCENT N2 DURING ACCELERATION. AFTER THE #2 ENG WAS SHUT DOWN; WE TAXIED CLR OF THE ACTIVE TAXI RTE. WHEN THE #2 ENG ROTATION HAD STOPPED; WE REENGAGED THE STARTER TO MOTOR THE ENG FOR ANOTHER PERIOD OF MIN 20 SECONDS AND INSURED EGT BELOW 100 DEGS. THE ENG WAS RESTARTED NORMALLY. ALL CHKLISTS WERE COMPLETED AND THE FLT PROCEEDED TO KDFW WITHOUT INCIDENT. UPON ARR KDFW; APPROPRIATE LOGBOOK ENTRY WAS MADE TO RECORD OVERTEMP CONDITION.