"cooling of relations" is correct and usable in written English.
It is often used to refer to a period during which two countries or people become less friendly or less cooperative with each other. For example: "After months of political tensions, the cooling of relations between the two nations appears to have had a positive effect."
The generally assertive course of his foreign policy also led to a cooling of relations with Germany.
A similar cooling of relations marked the beginning of the end of Italy's previous centre-left government.
This has stoked fears that any cooling of relations with Beijing could damage efforts to narrow the economic gulf between the south-east and the north of England.
The Aznar and Villalonga families are close, and Mr. Villalonga's marital problems have not helped a cooling of relations with Mr. Aznar.
The decision to defy the European court will no doubt contribute to a further cooling of relations between Poland and Europe.
Both Mr. Gordon and Mr. Melia were asked whether the expected return of Mr. Putin as president in March augured a cooling of relations.
Russia maintains very good relations with the United States, he said, and Clinton's criticism of Moscow's actions in Chechnya "was motivated by the wish to save Russia additional problems". "I would consider it absolutely incorrect to produce the impression that some kind of period of cooling off of relations between Russia and the United States has begun or is beginning," the prime minister said.
This episode led to a cooling of his relations with the patriarchate, and the temporary cessation of his visits to Moscow; he renounced the office of exarch over the radio.
The cooling of his relations with Tony Blair started when the British prime minister argued at a European summit last autumn that it was hypocritical for France to talk of alleviating third-world poverty while simultaneously blocking reform of the CAP.
Thus, if Ukraine and Georgia joining NATO is more important than the (presumably temporary) cooling of Russian relations with the West, then NATO will go ahead and make them members.
His plans to come to the United Nations and to tour the United States have not been al tered by the decision of Pre mier Aleksei N. Kosygin of the Soviet Union to stay away in the light of the present cool ness of relations with the United States.
