What was found
(CAN) TAIL 808 FLIGHT 7671 CREW RECEIVED A AUXILIARY BATTERY HOT INDICATION IN CRUISE. ACTIONING QRH AND DECISION WAS MADE TO DIVERT AIRCRAFT. AUXILIARY BATTERY TEMPERATURE CONTINUED TO CLIMB EVEN AFTER THE BATTERY WAS SELECTED OFF. EMERGENCY WAS DECLARED INBOUND TO QUEBEC. AIRCRAFT LANDED AND TAXIED TO THE GATE NORMALLY, CFR FOLLOWED THE AIRCRAFT TO THE GATE. MAINTENANCE PERSONNEL FOUND AUXILIARY BATTERY HOT AND AT FAULT. BATTERY REPLACED AND TESTED SERVICEABLE AIRCRAFT RETURN TO SERVICE.