It is perhaps interesting to also consider tea, and the transatlantic differences in language.
It's clear that in the US, people serve a cup of hot tea far more often than they serve a nice hot cup of tea.
I'd argue that this is probably because, in the US, people have been known to drink cold tea. Not just "cooled down from boiling with a little milk", not "just taken for a splash in Boston harbor", but, would you believe, tea to which they have added ice. They call it "ice tea", the 'd' having been accidentally struck out by a musket ball in the war of 1812. This is not an aberration of a few delinquents, either: it takes up about 85% of modern American tea drinking!
So, long story short, outside of New England, the term "tea" on its own, unqualified, typically means the iced variety.
So, to the American, the requirement is to differentiate from the more usual iced tea, so the term "hot tea" is used for clarity.
To the Briton, a "cup of tea" is more often a cuppa tea, and the nice hot cup of tea is in fact very slightly in the lead in recent years. Superlatives that serve no real purpose other than to emphasize the goodness of the offering, like "nice" and "hot" are often prepended to the compound term "cup of tea", rather than splitting it.
The same applies to coffee (and "ice coffee")