ENG FIRE WARNING; FO RETARDS THROTTLE. WARNING LIGHT GOES OUT CHKLIST ACCOMPLISHED EXCEPT CAPT ELECTS TO NOT LAND AT THE NEAREST SUITABLE ARPT. FO THINKS THE CAPT SHOULD LAND AS PER CHKLIST.

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THIS; TO ME; IS A CLASSIC COCKPIT RESOURCE MGMNT PROB. AFTER DEPARTING OAK AND CLBING TO OUR CRUISE FLT LEVEL; WE RECEIVED AN ENG #1 FIRE WARNING FOR APPROX 2 SECONDS. I WAS FLYING THE AIRPLANE (ON AUTOPLT) AND REACHED FOR THE #1 THROTTLE. AS I RETARDED THE THROTTLE TO IDLE; THE FIRE WARNING LIGHT WENT OUT. THE CAPT ASSUMED CTL OF THE AIRPLANE AND ASKED ME TO 'WORK' THE SIT. I BEGAN THE CHKLIST PROC AND GOT DOWN TO THE STEP WHICH STATES 'LAND AT THE NEAREST SUITABLE ARPT.' THE CAPT THEN STATED THAT EVERYTHING LOOKED OKAY TO HIM AND THAT WE WOULD CONTINUE TO OUR DEST. I TOLD HIM THAT I FELT WE NEEDED TO RETURN TO OAK. HE THEN ASKED A JUMPSEATER (A SENIOR COMPANY PLT) IF HE WAS COMFORTABLE WITH OUR DECISION TO CONTINUE TO OUR DEST. THE JUMPSEATER SAID THAT HE WAS COMFORTABLE WITH THE CAPT'S DECISION. THE CAPT'S OPINION WAS THAT WE DIDN'T GET ALL OF THE INDICATIONS OF A FIRE. THE WARNING WAS SO BRIEF; WE DIDN'T NOTICE AN ILLUMINATED FIRE HANDLE OR AN ILLUMINATED START LEVER HANDLE; AND NO ONE HEARD THE FIRE WARNING BELL. WE ONLY SAW A RED MASTER WARNING LIGHT AND RECEIVED A LEVEL 3 ENG #1 FIRE. THE FMS ALSO WENT INTO THE ENG OUT MODE. THE DISCUSSION CONTINUED IN THE COCKPIT FOR AWHILE; BUT THE CAPT FELT THAT EVERYTHING WAS OKAY. HE FELT THAT THE WARNING WAS A FAULT. I TOLD THE CAPT THAT I FELT THAT WE DIDN'T NEED ALL THE INDICATIONS -- A 'LITTLE WARNING' IS AS BAD AS A 'FULL BLOWN WARNING.' I ALSO RESENTED THE ASKING OF THE JUMPSEATER IF HE WAS COMFORTABLE -- I WASN'T COMFORTABLE. WE DID CONTINUE TO OUR DEST (3 HRS) AND LANDED WITHOUT FURTHER INCIDENT. WE ENTERED THE DISCREPANCY IN THE MAINT LOG.