Not the best way to go about it perhaps, but it works. Add the following filter to functions.php:

// Remove the automatic width and height on images added by WordPress
function remove_thumbnail_dimensions( $html, $post_id, $post_thumbnail_id, $size, $attr ) {
    $html = preg_replace( '/(width|height)=\"\d*\"\s/', "", $html );
    return $html;
}
add_filter( 'post_thumbnail_html', 'remove_thumbnail_dimensions', 10, 5 );