Before sci-fi started to become a feature of stories in the 1800s, are there any earlier examples of books, written as fiction, that are set ‘in the future’, with the improvements/changes that the author believes will, or theoretically could, happen in t+100 years or so? I’d ignore all prophecies ansd suchlike that were supposed to be literally true.
Technically, no, because modern scholars have retroactively inducted all earlier future stories into the field. 
The answer you want is yes, there were many such stories, of varying types and forms. I’m taking my information from the standard work on early sf, I. F. Clarke’s The Pattern of Expectation: 1644-2001.
The form as we might today consider science fiction appears to start in the late 18th century, with the publication of the anonymous The Reign of George VI in 1763 and the book that almost everybody credits as the real start of looking to the future in 1771, Sebastien Mercer’s prophecy of an ideal world L’An 2440. The latter was a major variation of the practice of setting utopias in far-off lands in the present.
But Clarke, being a scholar, looks for precursors of all sorts, tracing the form even farther back. Francis Cheynell wrote Aulicus his Dream, of the King’s Sudden Comming to London in 1644. This was during the English Civil War and predicted a future with Charles victorious.
Better from your point of view is Epigone, histoire du siecle futur, by Jacques Guttin in 1659. He created a future French world-wide empire as a backdrop for his romance tale.
When even Clarke calls a work “tedious, wordy and boringly repetitious” be glad that you never came close toSamuel Madden’s 525-page first volume (of six, the rest never written) Memoirs of the Twentieth Century, being original letters under George the Sixth, of a UK powerful over all.
Clarke wrote:
By 1800 you could also find similar works from Denmark, the Netherlands, and Germany, but even Clarke does no more than mention the titles.
In short, there were lots and lots of books predicting the future before Mary Shelley or Poe or Verne or whenever you want to start dating “modern” science fiction. I can pretty much guarantee that nobody but specialty scholars have even heard of any of these books, much less read them. The idea of the future as a predictable, and different, place is essentially a creature of the Enlightenment and that’s an 18th century development. Once started rolling, the bandwagon has never been empty.