my post doesn't discuss filtering the length of the search widget specifically. instead i tried to explain filters in general, b/c the process is the same, every, single time. once you get it you won't have to ask, how do i filter this? how do i filter that? b/c you will know how to simply filter. it took me a long time to get my head around it which is why i make a point to try to explain it to people.
so you want to change the search form length.... the first function in widget-extensions.php is thematic_search_form() and the very first line of said function is
$search_form_length = apply_filters('thematic_search_form_length', '32');
in my primer on filters i explained that apply_filters is your signal that you can filter that value, and that thematic_search_form_length is the filter's name.
then i go on to explain how to set up filter in order to change a variable. which adapted to your specific example should be:
short, sweet, elegant. that is how you filter anything.... take a value in, (not in this case since we don't need it), change it, pass it back.
hope that makes sense