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Discover Ludwig'cool head' is correct and usable in written English.
It is an idiomatic expression, often used to refer to a person's ability to remain composed or level-headed under pressure. For example, "When the project ran over-budget, John kept a cool head and managed to make adjustments to meet the deadline".
Dictionary
cool head
noun
A calm, focused demeanor and mindset; a person having such characteristics.
Exact(60)
She has a cool head.
IT TAKES a cool head to invest.
Chris always had a very cool head.
Can Kasparov keep a cool head?
Thomas Schaaf kept a cool head, though.
You have to keep a very cool head, an ice-cool head".
"He is a cool head in the middle.
Marine Le Pen admired his "cool head" and "economic vision".
We're trained to keep a cool head in emergency situations.
The president has a cool head; mavericks are hotheads.
I was able to keep a cool head.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com