The group met periodically to discuss climate mitigation efforts like switching to LED streetlights, retrofitting public buildings and generating energy from landfills. The William J. Clinton Foundation provided technical assistance and financing for discrete projects, but the group of cities, known as the C40, lacked a steady financing stream, a database of emissions and mitigation programs, and a professional staff.

Enter Mr. Bloomberg, who campaigned for and won the chairmanship of the group last year. He pledged $6 million a year of his foundation money for each of the next three years to bolster the C40 and essentially muscled aside the Clinton staff members working on the project. Mr. Clinton, never one to reject a gift horse, happily acceded.

“I really don’t care how you characterize it,” Mr. Clinton said. “The fact that he made a multiyear commitment coincident with his leadership means that we will be able to go in and help cities who are in trouble financially and can’t do these projects.”

An adviser to Mr. Clinton, who spoke on the condition of anonymity to elaborate more candidly on Mr. Clinton’s remark, was a bit less diplomatic about Mr. Bloomberg’s approach. “He came to us,” the adviser said. “What are we going to do, fight him? They have the money; the golden rule applies.” As in, he who has the gold, rules.

The Clinton-Bloomberg partnership comes at a tough time for those fighting climate change. Congress has made it clear that it is not going to enact a national program to address global warming any time soon and the 194-nation United Nations process has made little progress toward a binding international treaty.

Donors who have provided financing for climate programs are frustrated and fatigued, and many advocacy groups are turning their attention to issues on which they can have tangible impact. Organizations are consolidating and learning to make do with less.

Mr. Bloomberg refers to this as a “maturing” approach to activist philanthropy. “It’s not so much people getting bored with the whole thing or walking away,” he said. “It’s that if you’re going to live through the tough times, this type of efficiency makes sense.”