Hello,
You can publish the search module to any of the available positions here:
http://www.shape5.com/demo/cleanout/index.php/features-mainmenu-47/template-features/90-module-positionsThe reason the search was not coded into the "standard" position for this Template was due to the width constraints and the way this head bar was designed. It wouldn't fit properly or work with responsive with the width of the menu. I would suggest a position such as the top row or drop down positions for this. The only other option would be to custom program a brand new row into the Template below the menu bar and add a secondary menu and search functionality. You can use another Template with this option as a reference in the index.php file.
We don't provide support for these types of custom programming chnages via the forums unfortunately but let me know if you need any pointers.
Regards,