Customizing recent blog posts block
The block "Recent blog posts" is in blog.module.


/**
 * Implements hook_block_view().
 *
 * Displays the most recent 10 blog titles.
 */
function blog_block_view($delta = '') {
  global $user;

  if (user_access('access content')) {
    $result = db_select('node', 'n')
      ->fields('n', array('nid', 'title', 'created'))
      ->condition('type', 'blog')
      ->condition('status', 1)
      ->orderBy('created', 'DESC')
      ->range(0, variable_get('blog_block_count', 10))
      ->addTag('node_access')
      ->execute();

    if ($node_title_list = node_title_list($result)) {
      $block['subject'] = t('Recent blog posts');
      $block['content']['blog_list'] = $node_title_list;
      $block['content']['blog_more'] = array(
        '#theme' => 'more_link',
        '#url' => 'blog',
        '#title' => t('Read the latest blog entries.'),
      );

      return $block;
    }
  }
}


So there is no .tpl.php to customize. 
Using Views module to create a block which lists out recent blog posts would be a solution for you.

Hope this help,