[eluser]pickupman[/eluser]
Cron would be the way to go if it has to be on exact time increments, otherwise you could extend your controller class. Add a function call that deletes files before the time interval in your constructor. When ever a page is called, the controller will delete any files 24hours prior to now.
Take a look at one of the cache libraries out there. They basically automatically delete cache files after a set time interval. Search for Phil Sturgeon's cache library.