What was found
BRAKE DEICE VALVE OPENED SUPPLYING BLEED AIR TO BRAKE DEICE SYS WITHOUT BEING ELECTRICALLY ACTUATED VIA THE BRAKE DEICE SWITCH. (BRAKE DEICE INDICATION AND RT ENGINE TORQUE INDICATION CONFIRMED VALVE WAS OPENED.) ON CLIMB OUT, THE RT BRAKE DEICE ANNUCIATOR ILLUMINATED AND COULD NOT BE EXTINGUISHED. DUE TO THE HIGH AMBIENT TEMPERATURE FOR THAT DAY THE CREW DECIDED TO RETURN TO THE DEPARTURE AIRPORT RATHER THAN CONTINUING THE FLIGHT AND THE POSSIBILITY EXPERIENCING A OVERHEAT SITUATION IN THE WHEEL WELL.