Book burnings started in 1933, but did they continue on in 1935 and maybe beyond?
There was certainly a second round of "purifications" (Säuberungen) in Nazi Germany in 1935. Die Bücherei (the official Nazi journal for lending libraries) published these collection evaluation guidelines in 1935.
However, I've never been able to confirm what happened to the books that failed the new test. The obvious solution would have been to burn them, but I've never seen any reference to anything like the mass public book-burnings of 1933 happening in 1935. It is possible that the number of books which still remained in 1935 was just too small to provide the spectacle of a public book-burning.
The "web exhibit" When Books Burn by the University of Arizona Library is well worth investigating, not least because they have included an extensive list of the sources used to create the exhibit.
Yes there were.
Take for example the book burnings in April 1938 in Salzburg (shortly after Austria was annexed by Nazi Germany) where about 1200 books (mostly from jewish authors) were burned. To my knowledge, this was the last big book burning on the soil of the Third Reich before the war started. Source: Book Burning in 1938.
Furthermore, the Nazis confiscated a lot of books and stormed libraries in the areas that they occupied, for example, in Czechoslovakia or Poland. See for example: Lost libraries of the 20th century.
There were also a lot of books that disappeared during the war. Most of them due to libraries that were damaged during World War II, but it is not entirely known whether the Nazis burned some of them themselves.