Check the Codex. the_post_thumbnail accepts two parameters, the second of which is $attr— “attributes”.
the_post_thumbnail('full',array('title'=>'yay! a title!'));
The Codex entry for the_post_thumbnail is not clear on what is and is not allowed as an “attribute” but it appears to depend on wp_get_attachment_image and by filters applied by that function. title does work though. I checked.