B737 ENG FIRE WARNING ACTIVATED MOMENTARILY DURING LEVELOFF. ALL ENG INDICATIONS WERE NORMAL AND FLT CREW DIVERTED FOR PRECAUTIONARY LNDG.

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WE WERE ON OUR THIRD LEG OF THE DAY. THIS LEG HAD THE FO AS PF AND ME AS PM. APCHING FL230 I WAS INSTRUCTED TO CHANGE FREQ AND THE FO HAD HIS HAND ON THE THRUST LEVERS TO LEVEL OFF. CHANGING FREQ I SCANNED THE INSTS AND ALL INDICATIONS WERE NORMAL. AT THAT TIME I HEARD THE FIRE WARNING BELL. I IMMEDIATELY LOOKED TOWARDS THE PANEL AND SAW ENG #2 FIRE WARNING IN THE HANDLE LIGHT AND ENG #2 OVERHEAT LIGHT. AT THE SAME TIME I SAID 'ENG #2 FIRE' AND LOOKED AT INST PANEL (ALL ENG INSTS WERE NORMAL EGT WAS 568). SIMULTANEOUSLY; THE FO (WHO WAS AT FL230) REDUCED THRUST SETTING AND EVERYTHING EXTINGUISHED BY ITSELF (INCLUDING WARNING BELL). THIS ALL HAPPENED QUICKLY (1 SECOND; NO MORE THAN 2). INDICATION WAS SO BRIEF THAT I DIDN'T HAVE TIME TO LOOK AT MASTER CAUTION/FIRE WARNING LIGHTS AND TO CANCEL FIRE WARNING BELL. I CALLED FOR THE ENG FIRE CHKLIST AND CHKED IN ON OUR NEW FREQ REQUESTING TO STAY AT FL230. WE DIDN'T EXPERIENCE ANY ABNORMAL ENG READING; NO VIBRATIONS; AND NO ABNORMAL YAW. BECAUSE; WE DIDN'T HAVE ANY MORE WARNINGS (ENG FIRE WARNING EXTINGUISHED BY ITSELF INCLUDING ALARM BELL IN SO BRIEF TIME) I SWITCHED TO THE 'IN ALL SITUATIONS' CHKLIST AND PERFORMED FULL OVERHEAT/FIRE AND FAULT/INOP MULTIPLE TIMES. THEY TESTED NORMAL. ANALYZING THE PROB; WE ASSUMED MOMENTARY GLITCH IN THE SYS INDICATION. I CALLED FLT ATTENDANTS TO VISUALLY CHK THE R ENG. IN THE MEANTIME WE AGREED TO PROCEED AND AS A PRECAUTION LAND IN ZZZ. ARPT WAS APPROX 60 MI IN FRONT OF US AND LNDG IN THE SAME DIRECTION. I COMMUNICATED WITH DISPATCH VIA ACARS AND RADIO; BRIEFED FLT ATTENDANTS AND MADE ANNOUNCEMENT TO THE PAX. FURTHERMORE; ALL INDICATIONS; IN ALL THRUST SETTING WERE NORMAL. ANALYZING THE PROB AS A CREW WE DIDN'T PROCEED WITH THE ENG FIRE CHKLIST; INSTEAD WE PROCEED WITH 'IN ALL SITUATIONS' CHKLIST AND AS A PRECAUTION LANDED AT NEAREST SUITABLE ARPT UNEVENTFULLY. MAINT CHKED THE ENG IN ZZZ AND DIDN'T FIND ANY HISTORY OF THE EVENT AND SUBSEQUENTLY THE ENG RUN UP DIDN'T SHOW ANY INDICATION OF THE EVENT. I FOLLOWED MY BEST JUDGEMENT AND USED COMMON SENSE; COMBINED WITH YRS OF EXPERIENCE TO ANALYZE THE PROB. CONSIDERING THE TIME LENGTH OF FIRE WARNING INDICATION AS A FLICK; THE FACT THAT IT WAS EXTINGUISHED BY ITSELF; AND ALL OTHER INDICATIONS NORMAL; WE AS A CREW PROCEEDED WITH WHAT WE BELIEVED AT THE TIME WAS THE SAFEST ACTION. WE DECIDED TO LAND AT THE NEAREST ARPT AS A PRECAUTION WITHOUT DISCHARGING THE FIRE BOTTLE AND NOT SHUTTING DOWN THE ENG. THE DIVERSION TO ZZZ WAS UNEVENTFUL. I BELIEVE THAT MY ACTION WILL BE SUBJECT TO JUDGMENT IF I SHOULD FOLLOW STRICTLY INDICATION AS ENG FIRE AND PROCEED WITH ENG FIRE CHKLIST. WE ASSUMED THAT WE HAD MOMENTARILY GLITCH IN THE FIRE WARNING INDICATION AND LANDED AT NEAREST SUITABLE ARPT.