When somebody is winding you up and you are trying not to let them see how much they're winding you up, you're keeping your cool. When a situation is difficult or stressful, but you're not letting the demands of the situation affect you, you are keeping your cool. If you do finally explode, implode or crumble under the pressure of a situation, you 'lose your cool' and thus lose control of your emotions.
"If that prick keeps on winding me up, I'm gonna smack him."
"Hey, relax. He's doing it on purpose, Don't lose your cool or he'll know he's got to you."
He's like Batman and Superman but better. Pretty much the greatest guy to walk the Earth.
In fact, he's the coolest guy ever! If someone refers to you as "cool" just know that Commander Cool is commanding that cool that you have gotten. Also, he's the greatest. Again. He's nice, handsome, and awesome.
He shares "Coolest guy ever" rights with Miles Davis
Don't worry, if you try your hardest, you can be cool too. It's as easy as getting high. Which is as easy as being yourself.