Did some playing about, managed to get it working.
<?php
/*
Template Name: Festivals - United States
*/
?>
<?php get_header(); ?>
<div id="left_full">
<?php
$args = array(
'orderby' => 'name',
'order' => 'ASC',
'child_of' => '3592'
);
$temp_query = $wp_query;
$categories = get_categories($args);
foreach($categories as $category) {
query_posts("posts_per_page=1&cat=$category->cat_ID");
if (have_posts()) : while (have_posts()) : the_post();
echo '<div class="interview_item">';
echo '<div class="interview_thumb"><a href="#" rel="bookmark">'; the_post_thumbnail('interview-thumb'); echo '</a></div>';
echo '<h1><a href="' . get_category_link( $category->term_id ) . '" title="' . sprintf( __( "View all posts in %s" ), $category->name ) . '" ' . '>' . $category->name.'</a> </h1> ';
echo '</div>';
endwhile; endif;
}
$wp_query = $temp_query;
?>
</div>
</div>
<?php get_footer(); ?>