What was found
LEVEL 1 BRAKE DIFFERENTAL TEMP AT 30 MINUTES INTO FLIGHT FL380 SAT -56 BRAKE TEMP WHEEL 6 FLUCTUATING RAPIDLY BTWN 330-375. AT 40 MIN INTO FLIGHT LVL 2 BRAKE OVERHEAT ILLUMINATED MAX TEMP 575. COMPLIED W/QRH TEMP SUBSIDED TO APPROX 370 AND FLUCTATED THERE WITH LVL 1 BRAKE DIFF TEMP PERSISTING UNTIL 2:20 INTO FLIGHT. NO. 6 BRAKE TEMP HELD AT 300 ALL OTHER BRAKE TEMPS MATCHED AT -15 DEG THROUGHOUT. FOUND WIRE BROKEN ON THE NR 6 BRAKE TEMP SENSOR CONNECTOR. REPAIRED THE CONNECTOR IAW SWPM 20-31-00. BRAKE INDICATION READS NORMAL.