Handling sessions through cookies, is it safe?

I need to limit the session time for a particular user who is working
on my site. I'd also like to extend the session time each time user
performs some action (moves from one page to another). I've written the
following code to accomplish this task

/* Extending session */
if(isset($_COOKIE['username'])) {
setcookie ("username", $_POST['username'], time()+3600);
}

Variable $_COOKIE['username'] right after the authorization is
completed.
The problem is that I don't think this is a safe way to handle
sessions. Perhaps I should use $_SESSION global array to store the
username of the logged user?

.