EMB ERJ 145 ER/LR
Flight Crew Commercial
Workload; Distraction; Time Pressure
Aircraft Equipment Problem Critical; Flight Deck / Cabin / Aircraft Event Smoke / Fire / Fumes / Odor
Flight Crew Landed in Emergency Condition; Flight Crew FLC complied w / Automation / Advisory; General Declared Emergency
Aircraft
We were on with approach in the final segment of our flight from to ZZZ. Approach had cleared us down to 6;000 feet and as we were passing through 10;000 I started the APU in anticipation of deplaning at a hard stand.  As I started the APU I picked up the checklist to finish the approach check and when I glanced back at the EICAS I noticed the APU had hung around 55%. As I reached up and pressed the stop button the APU fire warning appeared. We were approximately 10 minutes from landing and were briefed and set up for the visual landing into ZZZ. As I discussed the situation with the First Officer I ran the QRH APU Fire In-flight checklist. At the completion of the checklist all indications showed the fire had been extinguished.  I decided that we would continue into ZZZ. The First Officer prompted me to advise the Tower; I then declared an emergency and had Tower scramble Fire and Rescue. I also advised the Flight Attendant of the situation.  The aircraft was exhibiting no problems and we were anticipating on a normal landing; but I wanted her ready to evacuate if need be.  Tower cleared us for XXR and we landed normally and pulled off onto the taxiway.  The First Officer requested the fire trucks to inspect our tail section for any sign of smoke or fire; while they did so he advised the passengers of the situation explaining the presence of the airport fire personnel to allay any concern they may have. We were given the all clear and taxied to the gate without incident and the passengers deplaned.I would suggest in this situation; stay calm and run the appropriate QRH.  We did so and the problem was rectified rather quickly. Make sure there is an environment where open communication flows freely so that everyone is on the same page.
Following an APU air start before landing; an EMB-145 APU Fire Warning alerted with the APU RPM hung at 55%; so an emergency was declared; the warning ceased when the QRH was completed and after landing no sign of a fire was found.