The phrase "a sort of cool" is correct and usable in written English.
It can be used to describe something that has a certain level of coolness or appeal, but not in an absolute sense.
Example: "The new café has a sort of cool vibe that attracts a lot of young people."
Alternatives: "kind of cool" or "a type of cool".
(The exception is Eliza, a sort of cool Cordelia).
But The Bell Jar had a sort of cool jauntiness to it.
A sort of cool, bland reason oozed from him, and until the last two weeks a certain political expediency seemed beyond him.
The snack was introduced in 1948, and since 1986 the brand's mascot has been Chester Cheetah, who today is a sort of cool troublemaker.
In a brilliant marketing partnership, Klout has announced that users with a score of 40 or higher can gain admittance to Cathay Pacific's First and Business Class Lounge at SFO, which looks very swanky in a sort of cool, I-work-in-the-Valley kind of way.
As a result, he achieves a sort of cool, tangible edition of pointillism.
DEEP DOWN inside, beneath a sort-of-cool, sort-of-not exterior, Michael Chang feels utterly ordinary.
Tyner's pianistic cascades of bright chromaticism come as a sort of cooling relief from Coltrane's blazing-hot performance but not a spark to it; they no longer add much in the way of underpinning to Coltrane's solos.
(To keep Isabella's milk from spoiling, No Impact Man tries to construct a sort of cooler out of clay pots and wet sand, but it doesn't work, so his wife ends up cadging ice from a neighbor).
Miki B. represent a sort of "city cool" aesthetic, while Kid's Club will encompass sporty athletic, modern casual, and classic preppy styles.
Anyway, here it was, flaunting an ersatz sort of cool with its stylish group of 1950s academics and artistic types gathered for a midsummer's eve party at a house on an island with no phone or neighbours and just the one unreliable boat should escape be necessary in the event of a woman being strangled.
