In 2007, Dr Barbara Frale discovered a document in the Vatican Secret Archive showing that Pope Clement V had privately absolved the last Templar master Jacques de Molay of all guilt. This followed an investigation by cardinals conducted in August, 1308 that included interviews with De Molay and other Templars. The actual document is viewable here on the Vatican archive website.
The papal absolution didn’t do the Templars much good as in public, the Pope went ahead and disbanded the Order largely under pressure from the French King. Frale, a respected academic, has written an excellent book on the document she found which you can buy here.