Retrieve the update link if there is a theme update available.

Will return a link if there is an update available.

Signature

get_theme_update_available( $theme )
theme
 (WP_Theme) WP_Theme object.

Return

(string|boolean) HTML for the update link, or false if invalid info was passed.

Source

function get_theme_update_available( $theme ) {
	static $themes_update;

	if ( !current_user_can('update_themes' ) )
		return false;

	if ( !isset($themes_update) )
		$themes_update = get_site_transient('update_themes');

	if ( ! is_a( $theme, 'WP_Theme' ) )
		return false;

	$stylesheet = $theme->get_stylesheet();

	$html = '';

	if ( isset($themes_update->response[ $stylesheet ]) ) {
		$update = $themes_update->response[ $stylesheet ];
		$theme_name = $theme->display('Name');
		$details_url = add_query_arg(array('TB_iframe' => 'true', 'width' => 1024, 'height' => 800), $update['url']); //Theme browser inside WP? replace this, Also, theme preview JS will override this on the available list.
19 more lines...
WP Trac GitHub

Link here