well, yes, you should see the thankyou.php page. if it is not directing to the thank you page, then either there is an error occurring, or the email code is not triggering.
try changing the following code in the contact us page:
if ((($_SERVER["REQUEST_METHOD"] == "POST") && (isset($_SERVER["HTTP_REFERER"]) && strpos(urldecode($_SERVER["HTTP_REFERER"]), urldecode($_SERVER["SERVER_NAME"].$_SERVER["PHP_SELF"])) > 0) && isset($_POST))) {
to:
if (isset($_POST["Contact_Name"])) {