Kilika Temple is located at the end of the Pilgrimage Road that leads through the Kilika Woods. While there, your team will need to complete the Kilika Cloister of Trials.
You can revisit the Kilika Temple at any point during your playthrough of the game. That said, you only technically need to visit it the one time as the team travels through Kilika on their way to Luca. Refer to the walkthrough and strategy guide section for more information: