I did some testing today at school with a current regulated PSU, and at 400mA, they were VERY bright and didn't warm up anything beyond what the aluminum core could easily dissipate.
Now, here's the really interesting part. Being as I ordered quite a few extra (and could get away with sacrificing a couple to the altar of science), I opened up the amperage and let the LED's do as they would. Both the cold white and warm white bars pulled ~500mA, and wouldn't draw any more, despite my de-regulating the current. Any theories? They also didn't warm up much more than at 400mA.