I make a tea how I make any tea I would drink, just in a stronger and larger quantity. Then I cool it down in the fridge. I've also placed it in the freezer to really chill it down before adding lye. Normally I do a mix of water/ice with my soaps, but I don't want to water down the tea so freezing it just a little before I add lye helps keep it closer to my preferred mixing temp without a crazy high temp spike first. I do the same with coffee.
I also use well water, so I'm not sure how distilled water might work different.