Technically speaking, all custody orders are temporary -- not permanent. Why? Because they are subject to change by either party, at any time, upon a showing of a significant change in circumstances -- of the child and/or the parents.
Unless stated otherwise on a court order, temporary custody orders do not expire. However, should circumstances change warranting a change of the custody order, then either parent is entitled, so long as the child is a minor, to return to court to request a change in the custody terms.
For example, a current custody order may reflect 50/50 physical and legal custody; however, let's say one of the parents needs to relocate to another state for employment purposes. At this point, the parties have two options: 1) stipulate to a change of custody -- with the court approving the stipulation (agreement); or, if parties can't reach agreement, then one party files a motion for a change of custody -- with the judge making the final decision.
In sum, as a general rule, there is no expiration on "temporary custody orders" as any orders relating to children are, in essence, temporary -- as the needs and circumstances of children and their parents invariably change with the passage of time.
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Temporary custody will when the child becomes an adult. Also, temporary custody will expire if the case is dismissed - which could occur if the case is not brought to trial (or otherwise resolved) within five years of the date of filing unless there is a temporary Child or Spousal Support order in place, or marital status has been bifurcated and severed.
Please note that this answer does not constitute legal advice, and should not be relied on, as each situation is fact specific, and it is not possible to evaluate a legal problem without a comprehensive consultation and review of all the facts and court pleadings filed in the case. This answer does not create an attorney-client relationship.