Using a widgets title in the class attribute

Hello. I was wondering if there is any way to use a widgets title, as a class attribute (or just about any other acceptable attribute for an H2 element), using a dynamic sidebar?

I currently only have the default sidebar code

if ( function_exists('register_sidebar') )
register_sidebar(array(
'before_widget' => '<li id="%1$s" class="widget %2$s">',
'after_widget' => '</li>',
'before_title' => '<h2 class="widgettitle">',
'after_title' => '</h2>',
));

Basically, I would like to make the final outcome of the widget title to be <h2 title="TITLE HERE" class="widgettitle">TITLE HERE</h2> instead of just <h2 class="widgettitle">TITLE HERE</h2>.

Is this possible?