NEW YORK — James Caan, whose explosive performance as the hotheaded Sonny Corleone in “The Godfather” produced some of the most memorable moments in movie history, died Wednesday at age 82, his family announced Thursday. A cause of death was not released for the Bronx-born actor. “The family appreciates the outpouring of love and heartfelt condolences and asks that you continue to respect their privacy during this difficult time,” reads the announcement on Caan’s official Twitter page. Caan’s death was mourned Thursday by members of “The Godfather” family, including Al Pacino, who starred as M…