A B757-200 ON TKOF WITH HIGH AMBIENT FIELD TEMP ENGS #1 AND #2 EXCEEDED EGT LIMITS CAUSED BY #1 ENG ANTI-ICE VALVE DEFERRED INOP OPEN.

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DEPARTED ZZZ AT NIGHT AS PNF WITH #1 ENG ANTI-ICE MEL'ED AT ABC WITH ANTI-ICE VALVE FAULTED. MEL CALLED FOR ANTI-ICE VALVE TO BE LOCKED OPEN AS MAINT PROC. BOTH CAPT AND I QUERIED MAINT ABOUT ADVISABILITY OF OPERATING IN ZZZ DURING THE SUMMER WITH ANTI-ICE ON. WE ALSO CONSULTED ACFT OPS MANUAL LIMITATIONS AND FOUND OUTSIDE AIR TEMP NOT A LIMITING FACTOR WITH ROLLS ROYCE ENGS BUT DID FIND A 'CAUTION' STATEMENT IN THE ACFT OPS MANUAL ABOUT OPS WITH ANTI-ICE ON WITH AMBIENT TEMPS ABOVE 10 DEGS C. MAINT TECHNICIAN'S RESPONSE TO ME WAS (PARAPHRASED) 'IT WAS NOT (OUR) JOB TO BE SECOND-GUESSING DISPATCH CTL AND/OR MAINT CTL ABOUT (THIS)....' SO; ON TKOF/INITIAL CLBOUT; THIS IS WHAT I BELIEVE HAPPENED: ON TKOF ROLL; AUTOTHROTTLES ON; MAX EPR SELECTED (PER MEL); ENGS INDICATED NORMAL. AT APPROX 1000 FT AGL; CAPT CALLED FOR CLB PWR AND AS I REACHED FOR THE CLB THRUST PUSH BUTTON; BOTH CAPT AND I VIEWED #1 EGT DISPLAY CHANGE TO RED (INDICATES EXCEEDENCE). CAPT RETARDED #1 PWR LEVER TO BRING EGT BELOW LIMITS. NATURALLY; AUTOTHROTTLES DROVE #2 THRUST LEVER TO COMPENSATE FOR LOST (OVERALL) THRUST AND THUS #2 ENG EGT EXCEEDED LIMITS AS WELL! CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE RPTR STATED WHEN MAINT WAS QUESTIONED ABOUT THE OP OF #1 ENG WITH THE ANTI-ICE VALVE INOP OPEN THEY BRUSHED IT OFF WITH NO POSITIVE ANSWER. THE RPTR SAID WITH THE HIGH AMBIENT FIELD TEMP AT TKOF WOULD MAKE #1 ENG OPERATE CLOSE TO LIMITS. THE RPTR SAID AFTER THE TEMP EXCEEDENCE OF BOTH ENGS MAINT CHKED BOTH ENGS PER THE MAINT MANUAL AND FOUND NO DAMAGE.