For Sunken Temple, do you exhaust or recycle a ruin to get its effect?

Sunken Temple's ability does not require you to exhaust or recycle a rune.

According to its card text, the ability is: "When you conquer here with one or more [Mighty] units, you may pay [1] to draw 1."

To use this effect, you simply pay 1 Energy from your Rune Pool at the moment you conquer. You do not need to perform an action on a specific rune (like exhausting or recycling it) as part of this ability's cost; you just need to have the required 1 Energy available in your pool.