The phrase "a cool distance" is correct and usable in written English.
It can be used to describe an emotional or physical separation that feels detached or unfriendly.
Example: "Despite their shared history, there was a cool distance between them that made conversation awkward."
Alternatives: "an aloof distance" or "a detached demeanor".
Shirley returned to class after a brief hiatus, keeping a cool distance from Tiffany.
These clothes were maybe more interesting because they looked at a cool distance from fashion.
But Mr. Bovell's elaborate structure tends to keep us at a cool distance from the characters.
Date-and-time-stamped scenes suggest the inexorability of Shamoto's decline, from which the director maintains a cool distance.
The art was new and conceptual, and it stood at a cool distance from in-the-streets activism.
This sense of the drama being annotated and interpreted as it moves along is true to the novel, but it keeps the story at a cool distance.
Saturday's men's games, meanwhile, as has been true of recent Final Fours, had a kind of unreality about them — the lights were brighter; the floor seemed twice-as-large as usual, with the crowd kept at a cooling distance; and the hoops were gleaming.
When preëxisting recordings are imposed on movies, they tend to have a cooling, distancing effect: we know, whether or not we recognize them, that they are emanating from another place and time.
It's almost as if she still needs to keep a slight cool distance from her own experiences.
These stories present - usually from a certain cool distance - the turns and tracks of life downtown among New York's artists, aspirants, dealers in art and whatnot, hustlers and hangers-on.
I would add that, when applying power meditation to one's personal life as well, to deal with emotional and relationship difficulties, that building one's willpower allows us to see and act more clearly, with a kind of cool distance, while still remaining present.
