How to use session variables in wordpress

Question

I have a big problem with Wordpress and can't find a solution.
I'm trying to make a value available from every *.php file.
I want with $_SESSION['session_id'] = $var; but I've read that in Wordpress Sessions are not available.
I've tried it but it looks like that my Session is only saved once and after page reload the value is gone.
On my second page I get the Session with $var = $_SESSION['session_id'];

I've tried it with session_start() in my init hook and on my pages too where I use the Sessions but no effect. Is there someone who has an idea who I can transmit my values from one page to another without cookies because I don't want the users to see the values.