CRJ FLT CREW EXPERIENCED NON RESPONSIVE AND OVERTEMPED #2 ENG DURING LEVELOFF FROM DSCNT. PERFORM QRH PROCS; SHUT DOWN ENG; AND CONTINUE TO NEARBY DEST.

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WHILE LEVELING OFF AT FL180; I BEGAN TO SMOOTHLY ADD THRUST. AS I ADDED THRUST WE HEARD A LOUD BANG AND THE AIRPLANE HAD A SIGNIFICANT SHAKE. I ALSO FELT THE ACTION IN THE #2 THRUST LEVER. AS WE CONTINUED TO ADD THRUST I FELT THE ACFT YAW AND NOTICED THE #2 ENG WAS NOT SPOOLING UP. THE #1 ENG RESPONDED NORMALLY. I CONTINUED TO ADD PWR TO THE #2 ENG. IT DID NOT RESPOND. I CONTINUED TO ADD THRUST TO THE #1 ENG AND LEVELED OFF. AT THIS TIME THE #2 N1 35%; THE N2 65%; ITT 725 DEGS. ALL OTHER INDICATIONS WERE NORMAL. I TRIED ON SEVERAL OCCASIONS TO ADD PWR TO THE #2 ENG; HOWEVER; IT DID NOT RESPOND. ONLY THE ITT RAISED SLIGHTLY. I PULLED THE #2 THRUST LEVER TO IDLE ON SEVERAL OCCASIONS AND THE ENG WOULD GO TO IDLE. WE DISCUSSED WHAT HAD HAPPENED AND POSSIBLE CAUSES AND SOLUTIONS. WE WERE BOTH CONCERNED THAT THERE WAS SOME TYPE OF DAMAGE DUE TO THE SIGNIFICANCE OF THE ACTION. WE WERE ALSO CONCERNED THAT THERE WAS A PROB THAT WOULD MANIFEST ITSELF LATER IN THE FLT; IE; FUEL; OIL; HYD LEAK AND/OR POSSIBLE FIRE. AT THIS TIME WE FELT THE BEST DECISION WAS TO SHUT DOWN THE ENG TO PREVENT A MORE SERIOUS PROB AT A LOWER ALT. WE PERFORMED THE SEVERE DAMAGE INFLT PROC AND QRH AS WELL AS THE SINGLE ENG ABNORMAL QRH. AT THIS TIME WE WERE APPROX 65-70 MI FROM ZZZ. WE CONTINUED ON TO ZZZ. WE HAD TO LOSE 18000 FT; RUN PROCS AND CHKLISTS. WE ALSO FELT THAT THE RWY AT ZZZ AT 10000 FT WAS SUFFICIENT AS WELL AS ZZZ'S CFR. WE DID DECLARE AN EMER AND CONTINUED ON. MY FO COMPLETED ALL QRH PROCS AND TALKED TO THE FLT ATTENDANT. WE COMPLETED A SINGLE ENG APCH TO THE RWY WITHOUT EVENT. WE HAD PREVIOUSLY INFORMED ZZZ OPS WE WERE GOING ON OUR WAY AND TO ADVISE DISPATCH AS WELL AS MAINT. AFTER LNDG I HAD CFR LOOK FOR FIRE OR DAMAGE OF THE #2 ENG. CFR STATED NO FIRE OR VISIBLE DAMAGE. WE CONTINUED ON TO THE GATE. THE PAX WERE CALM. THE FLT ATTENDANT; AS WELL AS MYSELF; MADE AN ANNOUNCEMENT. ONCE ALL PAX WERE OFF THE ACFT; I CONTACTED DISPATCH; MAINT AND HAD A CHIEF PLT PAGED. THE CHIEF PLT CONTACTED ME AND I EXPLAINED THE SITUATION. AS STATED EARLIER; OUR CONCERN WAS THE BEST OPTION TO COMPLETE THIS FLT SAFELY; KEEPING IN MIND TO MINIMIZE THE DAMAGE TO THE ACFT AS WELL AS THE ENG.