You can do this with the CookieCuller extension - https://addons.mozilla.org/firefox/addon/cookieculler/

Thanks Tony. It's great that there are people like yourself that are willing to spend the time helping us ignorants. For anyone else reading this you also have to uncheck "clear history when FireFox closes". Unlike I.E. If you clear the history you also clear the cookies regardless of what you have set Cookie Culler to do.

Tony, thanks again. You helped me very much.

You're welcome

You don't need an extension for this. Go to Tools > Options > Privacy (or Edit > Preferences > Privacy). Select Use custom settings for history from the drop-down menu if it isn't already selected. Uncheck Accept cookies from sites then click the Exceptions button, type the domain of that site and click Allow.

The downside of that approach is if a site needs cookies to function properly, you will have to accept cookies from that site, resulting in having to keep cookies for more sites than just the ones that were originally wanted. Using Cookie Culler allows you to accept cookies from sites, but removing them when you close Firefox, only keeping those that you want.