You can't do it without saving the output somewhere, so your temp dir plan is fine.
- Assign each new user a unique id, via md5() or sha1() or whatever.
- Pass the id to the simulator and have it create its output files in a subdirectory named by that id.
- Render the links and image HREFs according to that id..
- Write a cron to periodically purge the stale subdirs.
Each person will get their own output set, on an unguessable URL.