As reported to the FAA. Reports are unverified, and codes are left as the FAA publishes them.
What was found
AIRCRAFT NOT GROUNDED: PILOT REPORTS ON CLIMB OUT FROM TAKEOFF RECEIVED A HOT BRAKE INDICATION, ON #4 BRAKE. LOWERED THE GEAR AND TEMP INDICATION WOULD VARY BETWEEN 280-400* AFTER ABOUT 10 MINUTES WITH GEAR DOWN TEMPERATURE INDICATION WAS NORMAL. EMERGENCY WAS DECLARED AND FLIGHT LANDED WITHOUT INCIDENT. MAINTENANCE REMOVED AND REPLACED BRAKE TEMP MONITORING UNIT IAW AMM 32-47-18 AND #4 BRAKE TEMP SENSOR IAW AMM 32-47-15. OPS CHECK NORMAL.