As the title indicates, these three forms of words/phrases can be quite confusing to me sometimes. When should they be written as one word ("boilinghot"), when should they be written in two words ("boiling hot"), and when should they be written as a hyphenated compound ("boiling-hot")? Does it make any difference which is used? There are other terms like this, such as blackboard/black board/black-board; swingman/swing man/swing-man etc.
In the first place, I've never seen boilinghot used.
As for the other two, there are different times for different uses. Only use the hyphen when it is a compound adjective
Let's speak of why the sea is boiling hot.
Let's speak of the boiling-hot sea.
@drm65 illustrates how Google NGrams may be misapplied. Searching for a hyphenated expression will cause it to flat-line unless you put a space between the hyphen and the words: e.g. "boiling hot,boiling - hot"
So while boiling hot appears to be used more often than boiling-hot, the latter's representation is not zero.
Two words is most common and appropriate: boiling hot. Unless it is used as an adjectival phrase; in which case the hyphen is appropriate for delineating the extent of the phrase. Though this Ngram illustrates that the hyphen is even then largely neglected.
As an aside: almost all phrases like this have a preferred form. Blackboard is the preferred form of that phrase:
And for swing man:
Edited: as @Robusto pointed out in his answer, I had inadvertently used the wrong syntax in my Ngram charts. Needless to say, I fixed the problem as soon as I realized it. Thanks again, Robusto!