That's pretty easy.
Just use the following code in your child theme's functions.php:
funtcion remove_header() {
remove_action('thematic_header','thematic_brandingopen',1);
remove_action('thematic_header','thematic_blogtitle',3);
remove_action('thematic_header','thematic_blogdescription',5);
remove_action('thematic_header','thematic_brandingclose',7);
remove_action('thematic_header','thematic_access',9);
}
add_action('init', 'remove_header');
Now everything is gone and you can add your code:
function childtheme_header() {
<-- Here's your code -->
}
add_action('thematic_header','childtheme_header');
As I said .. no need to touch any Thematic file at all :-)
Cheers,
Chris