The way you describe a timeout makes sense. There can only be a meaningful interaction among both parties when emotions are under control. I also tell my kid to take a minute off and calm down first if necessary.
There was a german parenting TV show a few years ago where the host repeatedly made children of various parents sit somewhere alone until they cooled off. This is the first thing I thought of when cooldown was mentioned. It's somehow easier to be consistent that way: Yelling, hitting, swearing, whatever. The child will know what will happen next and hopefully avoid it.
But cooldown alone stops making sense, when it is used for everything. I think it's better to respond with a consequential task which makes sense according to the cause. Even though it is harder to find and follow through sometimes.