By definition, "warm blooded" means "produce their own heat" (obviously drastically simplified). I don't think it matters whether the coconut is on a deserted island or on the shelf at Woollies, it's still not warm blooded.
Mammals aren't "living organisms with fur and milk". They're "the most recent common ancestor of the echidna and the cat, and anything descended from that".
While "having fur and producing milk" may have been the original description of mammals, biology no longer classifies things that way.
Today, all of the classification is based on Clades, which can be established by doing DNA investigation (similarity matching). So, "mammals" are defined as a clade. And whether somebody falls into it or not depends on their DNA similarity. And coconut clearly do not belong into there.