Insert to wp_footer if widget is found in the sidebar

The constructor of widget is called when the widget is registered, so your add_action is called on (probably) every request. You can avoid that simply put the add_action inside widget() function, that is called only when the widget is printed so there is no need to check: just output what you want.

Also, if you need some context inside the footer method you can use a closure inside the widget method where you have easy access to $args and $instance variables (the first contain information about the sidebar and the widget id, the second contain informations on the fields setted for speficic widget):

class CustomWidget extends WP_Widget {

   function __construct() { 
      parent::__construct( 'my-widget-id', 'My Widget Name' );
   }

   function widget( $args, $instance ) {

    add_action( 'wp_footer', function() use ( $args, $instance ) {

      echo '<h1>' . $args['widget_id'] . '</h1>';
      echo '<pre>'; print_r( $instance ); echo '</pre>';
      echo '<pre>'; print_r( $args); echo '</pre>';
      echo '<hr>';

    }); 

   }

   function update( $new_instance, $old_instance ) {}

   function form($instance) {}

}

that makes the closure all the times the widget is added to page, i.e. if the widget is added 3 times, the closure will run 3 times.

If you want to prevent that use a static flag:

class CustomWidget extends WP_Widget {

   static $added = 0;

   function __construct() { 
      parent::__construct( 'my-widget-id', 'My Widget Name' );
   }

   function widget( $args, $instance ) {

    add_action( 'wp_footer', function() use ( $args, $instance ) {

      if ( static::$added !== 0 ) return; // run only once;
      static::$added++;

      echo '<h1>' . $args['widget_id'] . '</h1>';
      echo '<pre>'; print_r( $instance ); echo '</pre>';
      echo '<pre>'; print_r( $args); echo '</pre>';
      echo '<hr>';

    }); 

   }

   function update( $new_instance, $old_instance ) {}

   function form($instance) {}

}

^{PS: PHP 4 died a long time ago. Please use PHP 5 constructors…}