Temporary items work differently depending on where you get them. Besieged temps are only available during a Besieged and are lost when the fight is over. Ballista (if anyone actually does that any more) temps are the same. Abyssea temps are kept for when you return to Abyssea but are only available within Abyssea zones and cannot be used when you exit.

You cannot hold duplicates of temporary items, so any extra's you obtain are automatically lost. However, the list of items you can hold at any one time is pretty large so don't feel compelled to use them all up if they're not needed at the time.