Thats not your responsibility. If the user forgets to close the browser that is their problem. If you provide a logout button to close the browser that it is their responsibiility to click it.

A cookie check would be pointless as if they've left the computer then the page will not move and so the script can't check the cookie.

The only way is probably javascript to close the browser after x seconds but even that probably wont work as the user has to lcick ok for it to shut I think.