Just checking in.
But my guess is that the "cooler" has such a slick nickname because he's so cool and calm when his team doesn't need any production from him. To paint the picture: it's the top of the ninth, 0 outs, 3-1 count. The yankees are up 7-0 over the Devil Rays. He's sure to hit the 3-run homer then. If they're in Yankee stadium in October and the score is within 2 runs either way, he's surely going to strike out at every chance. At that point they probably call him the "cold". Who knows. But when he pouts in the dugout with Jeter, and they are on TV 57 times looking like their puppy just got run over (this never gets old) - those lips do look even more purple. good call.
Must be a combination of the above.