仅在搜索运行时输出文本

I have a custom post type that I'm searching through with a custom query. I want to output a message if there's too many results (that works fine). But the problem I have is when you first goto the page and no search has been performed, I don't want that message to appear. How can I stop it appearing when no search has been performed?

<?php $paged = (get_query_var('paged')) ? get_query_var('paged') : 1;

$args = array(
    'posts_per_page'    => 5,
    'post_type'         => 'researchdatabase',
    'post_status'       => 'publish',
    'paged'             => $paged
);

if($searchTerm != "") {
    $args['s'] = $searchTerm;
}

$the_query = new WP_Query($args);

if ($the_query->have_posts()) {
    $counter = 1; ?>

    <p>
        <b><?php echo $the_query->post_count; ?> research items</b>
        <?php if($the_query->post_count > 20) { ?>
            <br /><span class="research-alert"><b>Refine your search criteria to see fewer results.</b></span>
        <?php } ?>
    </p>
    <hr />
    <br />

    <?php while ($the_query->have_posts()) { $the_query->the_post(); ?>

        <?php // output results ?>

    <?php $counter++;
    } // end while

    // reset post data
    wp_reset_postdata();

} else {
    echo 'No results';  
} // end if
?>

Just change the condition:

<?php if($the_query->post_count > 20) { ?>

With:

<?php if($the_query->post_count > 20 && is_search()) { ?>

is_search() return true if any search term is sent for the current WP_Query.

"no search has been performed" equals "no search term in the query", why don't you just check search term first?

if(!empty($searchTerm)) {
    $args = array(
        's' => $searchTerm
        'posts_per_page'    => 5,
        'post_type'         => 'researchdatabase',
        'post_status'       => 'publish',
        'paged'             => (get_query_var('paged')) ? get_query_var('paged') : 1
    );

    $the_query = new WP_Query($args);
     // Your code.
}

BTW: if you want to display total count of search results, you should use $the_query->found_posts not $the_query->post_count it only count posts on first page.