How can I delete a temporary file associated with a user's session ID when he/she closes his/her browser?

It is very difficult (impossible?) to do that in a reliable way.

It's impossible. There is no real implementation of "the end of a session" - there is only a session ID that's passed on every request to the site (if at all). All you can do is run some code when the session times out, and you'll never know for sure wether a user has closed his browser, disabled cookies, moved to another site, or had his computer bust into flames.