Wordpress - Add class name to post thumbnail

Yep - you can pass the class you want to use to the_post_thumbnail() as part of the attributes argument, for example <?php the_post_thumbnail('thumbnail', array('class' => 'your-class-name')); ?>

Ref: http://codex.wordpress.org/Function_Reference/the_post_thumbnail#Styling_Post_Thumbnails

You can filter those classes.

function alter_attr_wpse_102158($attr) {
  remove_filter('wp_get_attachment_image_attributes','alter_attr_wpse_102158');
  $attr['class'] .= ' new-class';
  return $attr;
}
add_filter('wp_get_attachment_image_attributes','alter_attr_wpse_102158'); 

Add the filter just before you call the_post_thumbnail. The filter will remove itself automatically.

It is a bit of trek to get there but the_post_thumbnail uses get_the_post_thumbnail which uses wp_get_attachment_image which applies that filter.