A320 FLT CREW HAS ECAM WARNING FOR 'HOT BRAKES' AFTER TKOF AND BECOME DISTRACTED AND OVERSHOOT ASSIGNED ALT DEPARTING DEN.

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CAPT WAS FLYING. WE DEPARTED RWY 25 AT DEN. AFTER TKOF; ATC TURNED US TO A SOUTHERLY HEADING AND CLRED US TO 12000 FT. AS WE WERE LEVELING AT 12000 FT; WE RECEIVED A MASTER CAUTION AND A LEVEL 2 ECAM WARNING OF 'HOT BRAKES.' WHEEL BRAKE TEMP ON WHEEL #4 WAS 310 DEGS. FO AND I DECIDED TO FOLLOW ECAM PROC; SLOW TO BELOW 250 KTS AND LOWER LNDG GEAR. ABOUT THIS TIME; I NOTICED WE WERE SLOWLY PASSING 12300 FT AND RECEIVED AN ALT TONE. I IMMEDIATELY TOOK CORRECTIVE ACTION AND RETURNED TO 12000 FT. WE THEN TOLD ATC WE WANTED TO SLOW TO BELOW 250 KTS AND WE WERE CLRED TO DO SO. WE SLOWED AND DROPPED THE GEAR FOR 3 MINS UNTIL TEMP ON WHEEL #4 COOLED TO 285 DEGS. GEAR WAS THEN RAISED AND FLT PROCEEDED NORMALLY. ATC WAS ADVISED OF OUR PROB AND MAINT WAS CONTACTED TO ADVISE THEM OF THE HOT BRAKE PROB. HE ADVISED US THAT WE COULD CONTINUE ON TO PHX. CONCERNING THE HOT BRAKE PROB ITSELF; I FOUND IT UNUSUAL TO GET A 'HOT BRAKE' ECAM AFTER TKOF. IN 5 YRS OF FLYING THE A320; I HAVE NEVER SEEN THAT PROB SURFACE AFTER TKOF. THUS; I DID HAVE CONCERNS ABOUT A POTENTIAL WHEELWELL FIRE AND I WAS MOMENTARILY DISTRACTED WHICH LED TO THE ALTDEV. SUPPLEMENTAL INFO FROM ACN 583197: A PREVENTIVE ACTION WOULD HAVE BEEN TO IMMEDIATELY PLACE THE ACFT ON AUTOPLT DURING THE LEVELOFF. THE HOT BRAKES PROB ITSELF WAS CORRECTLY FIXED AND PREVENTED A POSSIBLE FIRE OR TIRE DEFLATION. ONE FACTOR INFLUENCING MY SLOWNESS TO USE THE AUTOPLT MAY HAVE BEEN DUE TO THE SMALL NUMBER OF FLT HRS IN THE PAST 90 DAYS.