'cold business' is correct and usable in written English.
It is an idiom and often used to describe a form of communication that is impersonal, lacking emotion, or lacking warmth, kindness, or compassion. For example, you could say "She has a cold business approach to customer service, with no attempt at friendly conversation."
Inevitably, a warm afterglow gives way to cold business.
When someone sells their home, it is not always just a cold business transaction.
That cold business logic has figured in a steady rise in recent years of new nonfiction about New York.
"We get genuine feminine satisfaction from turning the cold business of selling into a pleasant human relationship".
Clemens was treated like hired help at Yankee Stadium: appropriate applause when he won, vociferous boos when he struggled, a simple and cold business arrangement.
The real estate salesmen may complain about cold business leads in David Mamet's play "Glengarry Glen Ross," but the new Broadway revival of "Glengarry" is off to a very hot start at the box office.
Ken Berger writes on CBSSports.com that what James did was explode the last of the myth that this is anything but a cold-blooded business.
"When we work with our partners, it's not cut-throat, cold-blooded business deals that we are trying to strike," he said.
He should start by telling them that for all the giddiness of draft weekend, professional football can be a cold-blooded business.
"Deciding on a subject is mostly a cold-blooded business of weighing the subject against potential markets, timeliness, the availability of material, and the likelihood of getting the story, the kinds of factors publishers have to worry about," she explains.
Whenever pro sports executives implore players to essentially "Win one for the Gipper," my first inclination is to think about the day-to-day, cold-blooded business of an industry whose natural resource is muscle, healthy muscle.
