Yes, you will, if it expires.
For example, in C3C, if you build the Temple of Artemis, you'll get a free temple in every city. But when it expries, you lose all the temples in the cities that you got for free.
ie; If you have two cities, your Capital (which has a temple) and city X (which doesn't have a temple), when you build ToA, your Capital won't pay maintenance for the Temple it built earlier, and City X will get a free temple. But, when ToA expires, City X loses its free temple (no temple now) and your Capital will have to pay for its temple once again.