ACCEPTANCE FLC ON MD83 TEST FLT OVERTEMP #1 ENG DURING INFLT RESTART PROC.

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I WAS PF IN FO POS ON A COMBINATION CHK FLT AFTER DUAL ENG CHANGE AND DELIVERY FLT FOR SALE TO ANOTHER CARRIER. THE OTHER CARRIER'S CHK PLTS OCCUPIED THE CAPT AND JUMPSEAT POS. THESE 2 PLTS ARE OVER 60 RETIREES; AND THEIR JOB FOR THEIR CARRIER IS CHK FLTS AND DELIVERY FLTS. DURING THE EARLY PORTION OF THE FLT THEY ACCOMPLISHED MANY SYS CHKS TOGETHER WHILE I FLEW THE ACFT. IT APPEARED TO ME THAT THEY WERE COMPETENT AND REASONABLY PROFESSIONAL. ALL WENT VERY WELL UNTIL ENG SHUTDOWN AND RELIGHT CHKS. THE L MOTOR WAS PROPERLY COOLED AND SHUT DOWN. UPON RELIGHT ALL OF US NOTED STABLE IDLE ENG PARAMETERS. AS THE THROTTLE WAS ADVANCED ON THE L ENG; I RECEIVED A CALL FROM ATC AND WAS DISTR FOR 20-30 SECONDS. DURING THIS TIME I NOTICED THE ACFT WAS NOT PERFORMING AS WELL AS I EXPECTED IN A SINGLE ENG ENVIRONMENT AT FL230. I RECHKED THE ENGS AND FOUND THE L THROTTLE ADVANCED TO A HIGH PWR SETTING BUT THE ENG WAS STILL AT IDLE EXCEPT EGT WAS AT 730 DEGS. THE OTHER PLTS HAD NOT CONFIRMED GOOD ENG PERFORMANCE FOR THE L ENG ABOVE THE IDLE POS. IN ADDITION; I RECHKED THE R MOTOR TO FIND IT SHUT DOWN. THE OTHER PLTS HAD NOT ALLOWED THE R ENG TO COOL PROPERLY (3 MINS) AND HAD SHUT IT DOWN PRIOR TO CONFIRMING PROPER OP OF THE L ENG. I CONTACTED ATC AND OBTAINED A LOWER BLOCK ALT TO ALLOW TIME TO RELIGHT THE R ENG. I TOOK CTL OF THE RELIGHT PROCS AND THE R ENG RELIGHT WAS SUCCESSFUL TO NORMAL OP. DURING THE RETURN TO SEA THE L MOTOR ACCELERATED AND OPERATED NORMALLY ONLY AFTER WE ATTAINED APPROX 290 KTS IN THE DSCNT. REST OF FLT WAS UNEVENTFUL. HUMAN FACTORS: 'COMPLACENCY' -- THE 2 OTHER PLTS SEEMED TO KNOW THEIR JOB. 'TEAM BUILDING' -- I FAILED TO RECOGNIZE THEIR PROFESSIONAL LIMITATIONS. 'WORKLOAD MGMNT' -- WE FAILED TO PRIORITIZE TASKS AND ALLOW TIME FOR TASK ACCOMPLISHMENT. (I ALLOWED A DISTR AT A CRITICAL TIME.)