You could create your own widget that queries posts from a certain category then displays the_post_thumbnail in an unordered list linking to the post.
Example widget (add to functions.php):
<?php
class c3m_thumbnail_posts extends WP_Widget {
function c3m_thumbnail_posts() {
$widget_ops = array( 'classname' => 'thumbnail-posts', 'description' => 'Displays post thumbnails' );
$control_ops = array( 'id_base' => 'c3m-post-thumbnail' );
$this->WP_Widget( 'c3m-post-thumbnail', 'Post Thumbnail Widget', $widget_ops, $control_ops );
}
function widget( $instance ) {
echo $before_widget;
?>
<h2>Title Goes Here</h2>
<?php
$args = array(
'cat' => 16, //Replace with category ID of posts to show thumbnail for
'posts_per_page' => 6 //Replace with number of posts to show use -1 for all
);
$thumbnail_query = new WP_Query( $args ); ?>
<ul class="sidebar-thumbnails">
<?php
while ( $thumbnail_query->have_posts() ) : $thumbnail_query->the_post(); ?>
<li><a href="https://wordpress.stackexchange.com/questions/24506/<?php the_permalink(); ?>"><?php the_post_thumbnail(); ?></a></li>
<?php endwhile; ?>
</ul>
<?php
echo $after_widget;
}
}
To modify what posts are used see WP_Query class in the codex.