As for your specific claim about cookies, there is a little checkbox labeled "Keep me logged in" or "Remember me" on the login page. If you don't trust the terminal, don't check that box. Leaving it unchecked will set the personally identifiable cookies to expire at the end of your browser session.
This is the same advice given for any website about unsafe terminals, and anyone who has 15 years of security industry experience would be aware of cookie expiration. What exactly are you claiming here?