How to prevent Gmail from logging in when I am in private session?

How to prevent Gmail from logging in when I am in private session? I use Firefox in the private mode because I use a public computer. This I thought would eliminate all cookies, history and passwords between sessions. But I am finding, time and again, that Gmail does not ask me for my password when I restart my browser; it automatically logs me in.
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bert [Entry]

You can have Firefox automatically destroy your cookies and history at the end of every "browsing session", if that's what you're looking for. There are also a few add-ons that allow for the easy management of cookies on a site-by-site basis, such as CookieSafe or CookieCuller.