Not probably in the same way we think of it today. Can only speak for the Christian West, but for most people the underlying assumption was that eventually Christ would come again, and then the world would end and souls would end up either permanently in heaven or permanently in hell, see the Book of Revelations for more details. In that respect, given what medieval Christians thought the future would be like, there are plenty of paintings of the Last Judgment and the Apocalypse, some of which (Hieronymus Bosch) approach Lovecraftian. It's not clear to me that people really thought about "the future" in terms of technological and human advancement until much later. An early 17th century English noblewoman, Margaret Cavendish, wrote something that is sometimes called the "world's first science fiction novel", The Blazing World, but it appears to be set in a utopia or parallel universe rather than a future.