If the contact page is identified solely by the associated template, you can query for a page with the template name in meta key _wp_page_template
:
$args = array(
'post_type' => 'page',
'posts_per_page' => 1,
'meta_query' => array(
array(
'key' => '_wp_page_template',
'value' => 'contact_template.php'
)
)
);
$contact_page = new WP_Query( $args );
if( ! empty( $contact_page->posts ) )
echo get_permalink( $contact_page->post->ID );