No. The session ID is stored in the cookie, but that is all. This is then sent to the server every time a page is requested, and then the corresponding data is brought from the depths of PHP...
As long as you make sure that any important data is not stored in cookies in an unencrypted form, then you should be fine. Even when you use cookies, load and destroy is the approach I take. Load them into session, and destroy if they are no longer neccessary.