"heaven" is distinct from "sky"

In English, yes (but see below). Not so in German:

For both terms, the same word "Himmel" is used. Some words are derived from "Himmel", relating either to heaven or to sky. "himmelblau" means "blue as the sky", with absolutely no religious context. "himmlisch" can be roughly translated as "like in heaven", originally used in religious contexts, but often also just as "very good, could not be better", with no intentional religious context. "himmlischer Vater", like "Vater im Himmel" (father in heaven), is a formal christian term to address the christian god, used almost exclusively in that context.

What does that do to christian children (and children growing up in a christian environment)? Well, for many children, there is (initially) no difference between "Himmel" meaning heaven and "Himmel" meaning sky. This is amplified by using the euphemism "er/sie ist jetzt im Himmel" (he/she is now in heaven) for dead people, and by suggesting that they have become angels. So, many children more or less believe that heaven is somewhere in the sky. Rammstein has composed a song called Engel that picks up this idea and dissects it.

Where does it come from? My guess is Martin Luther's translation of the Bible, as that happened for many other terms as well. Luther's translation had a massive influence on the German language and culture.

A note on the term "heaven": Wikipedia mentions that "heaven" can also mean "sky". Merriam-Webster adds that especially the plural form "heavens" can also mean "sky".

Alexander