What was found
DEPARTED CAE EN ROUTE TO DTW. CLEARED TO FL 300, PASSING FL 240 EICAS CAUTION MESSAGE HYD 2 HI TEMP CHECKED SYSTEMS PAGE AND CONFIRMED HYD 2 HI TEMP IN EXCESS OF 135C. CONDITION CONFIRMED, QRH INITIATED. CONTACTED ATC, ADVISED OF SYSTEM PROBLEM AND COORDINATED STOP CLIMB AT F250. COMPLIED WITH QUICK REFERENCE HANDBOOK, CONFIRMED TEMPERATURE IN EXCESS OF 135 AND FOLLOWED PROCEDURES FOR ENGINE SHUTDOWN, AND SINGLE ENGINE LANDING. EMERGENCY DECLARED, NEAREST SUITABLE LANDING GREENSBORO, NC, ADVISED ATC AND DISPATCH AND WAS REDISPATCHED TO GSO. REQUESTED CRASH, FIRE, RESCUE MEET US ON LANDING. UNEVENTFUL LANDING GSO, TAXIED TO GATE WHERE PASSENGERS WERE DEPLANED NORMALLY AND ACCOMMODATED ON OTHER FLIGHTS TO DESTINATION. COORDINATED WITH DISPATCH, MOC, SOC AND LOCAL MAINTENANCE UNTIL RELEASE AT 1945Z. ASSISTANT CHIEF PILOT AND DTW OPS MANAGER ALSO ADVISED OF ACTIONS. MTX RAI NR 2 HYD RESERVOIR IAW CRJ AMM 29-11-32-400-802 OPS AND LEAK CHECK GOOD.