Why was the Concorde painted white and not black?
There is a discussion on it here that's worth reading but in short the requirements were just different. A few of the key points, 


The black color on the SR-71 offered some night camouflage in addition to its heat dissipation
The Concorde had an Aluminium airframe while the SR-71 had a primarily titanium airframe which could lead to different coating types.
The Concorde was a commercial aircraft many of which are often painted white thermal benefits aside they may have simply been keeping with what they usually did. 
The SR-71 flew substantially faster than the Concorde and had different thermal requirements. 
The hottest point on the Concorde was the nose 127&deg;C which was actually cooled by fuel being pumped through as a coolant. The hottest point on the SR-71 was the cockpit window which cooked in at 327&deg;C again, very different requirements thermally.