Work for you 
But if your religion is dead, that may still work for your current religion

If by temples, you mean Holy sites.. I think they still follow their original religion and probably keep spreading it.. There are 2 reasons I believe that is the case:
1. In a previous game I destroyed an opponent and conquered all his cities, at that point his religion had 0 followers anywhere but the holy sites were kept. later that game I found his religion taking a big portion of the city's territories.
2. In the religion screen, When you hover over each religion, It will tell you how many holy sites it has and in which empires do they exist. So in this case you will find some of them in your empire.
So I think the holy site follows the state religion of its founder probably at the time of starting the construction. It will probably keep its religion even if the founder changed the state religion. (Not tested)

Edit: After testing, the holy site follows the state religion of its founder at the time of completing the construction not at the time of starting it. Even If it is "Stone Rings" while your religion uses "Obelisk of the Gods".

Holy Site: State religion of finisher at time of finishing

Regular Faith districts (EQs): Current State Religion of Current owner