A320 FLT CREW; FOLLOWING HOT BRAKES ECAM PROC; RETRACT GEAR ABOVE MAX INDICATED AIRSPD LIMIT.

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I HAD BROUGHT THE PLANE IN FROM MDW FOR A 45 MIN TURN. THE BRAKE TEMP WAS FAIRLY LOW (150 DEGS) WHEN WE DEPARTED THE GATE AND I COMMENTED TO THE FO THAT I WOULD TRY TO BABY THE BRAKES AS WE WERE AT MAX GROSS FOR THE RWY 17L AT DEN. I DID HAVE TO GO DOWNHILL ON 'ED' AND FOLLOW A B767-300 WHO WAS TAXIING SLOW; SO I DID HAVE TO USE THE BRAKES. TEMP AT TKOF WAS APPROX 200 DEGS. THE TKOF WAS UNEVENTFUL AND WE CLBED TO 10000 FT. PASSING THROUGH 7000 FT WE RECEIVED A CLRNC TO CLB TO FL230 AND EXPEDITE THROUGH 12000 FT. I STAYED AT 'GREEN DOT' APPROX 210 KTS TO DO THIS. AS WE WERE PASSING THROUGH 12500 FT AND ACCELERATING THROUGH 280 KTS; WE RECEIVED A BRAKES HOT ECAM. I INSTRUCTED THE FO TO ACCOMPLISH THE ECAM BUT I FIRST DECELERATED BACK BELOW 250 KTS (MAX GEAR EXTEND SPD). I ALSO COMMANDED HIM TO ADVISE ATC OF OUR SPD AND LET THE PAX KNOW WE WERE GOING TO EXTEND THE GEAR. I COMMANDED GEAR EXTENSION AND COOLED THE GEAR FROM 320 DEGS BACK TO 285 DEGS. WE WERE CAUSING A JAM UP BEHIND US ON DEP DUE TO OUR AIRSPD AND IN MY HURRY TO GET BACK TO NORMAL SPD; COMPLETELY FORGOT THE MAX GEAR RETRACT SPD OF 220 KTS. I COMMANDED THE FO TO RETRACT THE GEAR AT 240 KTS. IT WAS SLOW AND NOISY TO RETRACT AND WE BOTH COMMENTED ON THIS AND THEN WE BOTH REALIZED OUR SPD ERROR. ALL INDICATIONS WERE NORMAL AND WE ADVISED MAINT CTL THROUGH ACARS. MAINT CTL ADVISED US THAT THE ACFT WOULD REQUIRE A VISUAL INSPECTION PRIOR TO DEPARTING MCO. HUMAN FACTORS PLAYING INTO THIS WAS THE PERCEIVED BACKING UP OF DEP TFC AND HURRYING A PROC WITHOUT REALLY THINKING IT THROUGH. THE ECAM ALSO DID NOT DISCUSS MAX SPDS FOR RETRACTION AND LOWERING.