Art historian Robert Farris Thompson has argued that the notion of "cool" (in the sense that you describe) had its origins in West African culture. In many African languages, the quality of being "cool" (as a metaphor relating to temperature) was correlated with an aesthetic sensibility: particularly a calm, effortless and serene attitude toward performing difficult tasks.

According to some sources, the first appearance of this kind of "cool" appeared in a 1884 article on "Negro English" by an American professor named James A. Harrison. In a list of "Negro" expressions, he included the phrase "Dat’s cool!", although he did not provide a definition.

The phrase subsequently appeared in jazz and blues songs in the early 20th century, such as Cool Kind Daddy Blues.

In the early 1930s, Zora Neale Hurston described a male character in her short story "The Gilded Six-Bits":

And whut make it so cool, he got money 'cumulated. And womens give it all to 'im.

By the 1940s, the phrase was solidly engrained in jazz culture - hence the phrase "cool jazz", which was associated with the nonchalant, worldly, self-confident style of Miles Davis and other musicians.

Cultural historian Peter Steans, on the other hand, has made the case that this understanding of "cool" was part of a broader cultural change in which Americans adopted a more restrained, repressed emotional style than did their Victorian ancestors.

Sources:

• http://www.jstor.org/stable/3334749?seq=1#page_scan_tab_contents (see also the book, Flash of the Spirit)

• http://www.slate.com/articles/life/cool_story/2013/10/cool_the_etymology_and_history_of_the_concept_of_coolness.html

• Peter N. Stearns, American Cool: Constructing a Twentieth-Century Emotional Style (NYU Press, 1994)