Without access to cron
you only have one option -- manage file cleanup on your own.
This is, in fact, what the PHP SESSION
handler does -- it creates a file of session data. Then, when PHP starts, there is a small chance that it will go through an remove expired files. (IIRC, there is a 1/100 chance that it will.)
Your best bet is to create a directory to store your temp files in and then use a similar process.
This might give you some ideas: Session Configuration