ACFT EQUIP PROB. ACR HAS TO SHUT DOWN ITS #2 ENG WHEN ITS OIL SYS OVERTEMPS.

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DURING CRUISE AT 31000 FT #2 OIL TEMP GAUGE ROSE TO THE YELLOW CAUTION RANGE; ON A SCHEDULED B-727 PAX FLT. 15 MINS IS ALLOWED IN THE YELLOW BEFORE INITIATING ABNORMAL CHKLIST; WHICH WE DID. AFTER DELEGATING FLYING; NAV AND ATC COMS TO THE FO; THE CAPT AND SO PROCEEDED WITH THE CHKLIST. THE CHKLIST CALLS FOR INCREASING PWR ON THE AFFECTED ENG IN ORDER TO INCREASE FUEL FLOW; WHICH MIGHT COOL DOWN THE OIL. THIS DID NOT WORK. INSTEAD THE #2 OIL TEMP INCREASED TO ABOVE MAX LIMITS. THE CHKLIST THEN CALLS FOR THE SHUTDOWN OF THE AFFECTED ENG. WHEN THE THROTTLE WAS PULLED BACK TO IDLE THE LOW OIL PRESSURE LIGHT ILLUMINATED AND THE OIL PRESSURE AND QUANTITY GAUGES DECREASED TO BELOW MINIMUM LIMITS. WE CONTINUED WITH THE CHKLIST AND SHUT THE ENG DOWN. WE HAD JUST PASSED DIXON AND WERE HEADED OUT OVER THE WATER ON AN ATLANTIC RTE TO FLL; FL. WE OBTAINED A RERTE CLRNC FROM ATC TO BACK OVER THE LAND AND REQUESTED A LOWER ALT; SINCE WE WERE HVY AND HAD SHUT DOWN 1 ENG. ATC GRADUALLY CLRED US TO FL220 WHERE THE AIRPLANE WAS PERFORMING WELL ON 2 ENGS. WE STARTED TO CONSIDER LNDG AT AN ALTERNATE ARPT ALONG THE RTE AND CONTACTED DISPATCH FOR ADVISE. THEY ADVISED US TO CONTINUE TO DEST IF EVERYTHING LOOKED OK. WE WERE STILL VERY HVY. IMMEDIATE LNDG WOULD HAVE REQUIRED DUMPING FUEL OR AN OVERWT LNDG. ALSO FINISHING THE REQUIRED CHKLISTS INCLUDING THE 1 ENG INOP APCH AND LNDG CHKLIST WAS GOING TO TAKE SOME TIME. BY THAT TIME WE WOULD BE NEAR JAX; FL. AFTER CHKING THE WX AT DEST AND DISCUSSING AND EVALUATING THE SIT WITH THE CREW; WE CONCURRED WITH DISPATCH'S ADVISE TO CONTINUE TO DEST. BY THEN WE HAD BURNED ENOUGH FUEL TO BE DOWN TO OUR MAX LNDG WT. THE AIRPLANE WAS FLYING WITH NO DIFFICULTIES; ALL SYS OPERATED NORMALLY; ALL ATC CLRNCS WERE COMPLIED WITH; NO EMER WAS DECLARED; NO SPECIAL HANDLING REQUESTED AND THE LNDG WAS UNEVENTFUL.