Dear Rich Staff reports that the use of copyrighted cover art on merch is an infringement and one that is highly unlikely to be excused as a fair use. The copyright is owned either by the publisher or cover artist.
Lowering Risks. You're totally safe to use cover art published in the U.S. before 1923 (public domain). You may also be safe using cover art published between 1923 and 1964 because a large percentage of works from that period were never renewed and fell into the public domain. (You can learn how to research renewals here). After 1964, most cover art is likely to be protected under copyright. Of course, there's always the possibility that a publisher has gone out of business, the cover artist has passed away, or nobody cares about the reproduction, and there is nobody interested in going after you (the orphan works syndrome). Non-merchandise thumbnail uses of book covers for purposes such as this blog are likely to be fair use.