B777 CREW HAD CARGO FIRE WARNING IN ZFW CLASS E AIRSPACE.

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CLBING OUT OF ABOUT 13000 FT; EICAS INDICATED FORWARD CARGO FIRE. NOTIFIED ATC; LEVELED AT 14000 FT; AND BEGAN CARGO FIRE CHKLIST. CAPT ASKED FOR AND OBTAINED CLRNC BACK TO DFW AND DSCNT TO 10000 FT. FUEL DUMP WAS INITIATED. FIRE WARNING REMAINED ILLUMINATED AND AN OPPOSITE DIRECTION RWY 17R LNDG REQUESTED. ACCOMPLISHED OVERWT LNDG CHKLIST AND EMER LNDG CHKLIST. DUMP TERMINATED AT 1000 FT SMOOTH LNDG ACHIEVED. STOPPED ON RWY. NO SMOKE OBSERVED BY FIRE AND RESCUE. TAXIED CLR OF RWY AND SHUT DOWN ENGS. MAINT; DISPATCH AND RAMP CTL NOTIFIED. TOWED BACK TO THE GATE. SUPPLEMENTAL INFO FROM ACN 501252: WE GOT A FORWARD CARGO FIRE WARNING EICAS MESSAGE CLBING THROUGH 14000 FT ENRTE TO FL180. WE IMMEDIATELY LEVELED OFF; DECLARED AN EMER; AND DIVERTED TO DFW REQUESTING ARFF TO STAND BY. FLT ATTENDANTS WERE BRIEFED ON THE NATURE OF OUR EMER AND THAT WE WERE NOT PLANNING A GND EVAC BUT THAT IT MIGHT BE NECESSARY ONCE WE LANDED. WE LANDED OPPOSITE TFC ON RWY 17R; BRAKED TO A STOP; AND WE ASKED ARFF TO CONFIRM WHETHER WE HAD ANY FIRE INDICATIONS IN THE FORWARD CARGO COMPARTMENT. WE STILL HAD THE FIRE WARNING. IT TOOK US 13 MINS TO TURN AROUND AND LAND. NO CONFIRMATION WAS NOTED. WE PULLED OFF THE RWY; SHUT DOWN BOTH ENGS; AND TREATED OUR HOT BRAKE CONDITION BY COORDINATING WITH THE FIRE MARSHALL AND MAINT. THE FIRE DEPT PUT FANS ON THE BRAKES; SEVERAL OF WHICH WERE SMOKING. AFTER ABOUT 30 MINS; WE WERE TOWED BACK TO THE GATE AND THE PAX DEPLANED. WE ALSO DUMPED FUEL PRIOR TO LNDG; ABOUT 55000 LBS.