No cookies, no querystrings? To modify something said in the US, "Up the Jordan without a paddle."
That's like saying "how can I greet 5000 conference attendees by name without the use of name tags?" The server keeps track of each browser by a] assignment of a cookie or b] propagation via the URL. There are other methods, I suppose, but they are usually dependent on running PHP code on the server, which you say you don't want to do. How 'bout auto_prepend'ing a header file that carried the sessid?
I suppose you could try some common Javascript include that passed the var along, or write the supposed IP (what is it $_SERVER['REMOTE-ADDR']?) of the user into a db or flat file, and then if that IP hit the PHP page again, you'd look up the session ID and set it with session_name(), but we're getting way out on a limb here...