Hi there, you could accomplish this by creating a child theme and then adding a new category.php template with a featured image added to it. The new category.php template file then override the archive.php file which currently controls the display of category pages.
Making a child theme means your changes won’t be overwritten when you update the theme. If you’re new to child themes, you can explore these guides:
http://codex.wordpress.org/Child_Themes
http://op111.net/53/
http://vimeo.com/49770088
Here’s the Codex guide to adding a featured image to a template file:
http://codex.wordpress.org/Function_Reference/the_post_thumbnail
You can also learn more here about the WordPress template hierarchy:
http://codex.wordpress.org/Template_Hierarchy
I’m not sure how comfortable you are with editing theme files and creating child themes, so let me know if you need further help after setting up your child theme.
