B737-500 ACFT EXCEEDS THE EGT PARAMETERS FOR TKOF CONSIDERATIONS AT SLC; UT.

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AFTER LNDG ORD; CAPT WAS CALLED BY MAINT CTL AND TOLD THAT BOTH ENGS HAD EXCEEDED EGT LIMITS FOR THE ENGS. #1 ENG WAS AT 953 DEGS C FOR 10 SECONDS AND #2 ENG WAS AT 963 DEGS C FOR 16 SECONDS. ON TKOF; THE AUTOTHROTTLE WAS ON AND WE DID A MAX PERFORMANCE TKOF FOR PERFORMANCE LIMIT. MAINT CTL SAID OAT (OUTSIDE AIR TEMP) 81 DEGS F AND I THINK IT WAS AROUND 21-22 DEGS C. AFTER PUSHING TOGA BUTTON; THE AUTOTHROTTLE OVERSHOT N1% BY 2% BEFORE CATCHING ITSELF AND SETTING THE CORRECT N1%. TKOF WAS NORMAL AND AFTER THE V1; VR; V2 CALLOUTS; I WAS LOOKING OUTSIDE FOR TFC AS WE WERE GIVEN A 280 DEG HDG; AND DID NOT SEE THE RED LIGHTS ASSOCIATED WITH THE OVERHEAT. THE OVERHEAT MUST HAVE HAPPENED BTWN LIFTOFF AND REDUCTION OF CLB PWR AT 800 FT AGL; AND CAME BACK WITHIN LIMITS AFTER PWR REDUCTION. MAINT CTLR SAID THESE ENGS WERE ORIGINAL ENGS WITH 28000 HRS. SUPPLEMENTAL INFO FROM ACN 582945: MAINT CTLR SAID ENGS WERE THE ORIGINAL ENGS ON THIS ACFT AND HAD MORE THAN 28000 HRS. HE ALSO SAID THAT THEY WOULD NEED TO BE CHANGED. I AM SURE THAT THE ENGS DID NOT EXCEED 930 DEGS UNTIL AFTER AIRBORNE; THEN CAME BACK WITHIN LIMITS AFTER CLB PWR WAS SELECTED. I FEEL THESE ENGS WERE WORN OUT AND THE RIGHT COMBINATION OF HIGH ALT AND HIGH TEMP AT MAX PWR CAUSED THIS EXCEEDANCE.