That's not my experience. I've gotten pepper at 24C (Haven't tried like 22, or 26, only 24 since it worked" from the start). At 20C it's pretty boring to be honest. I can recognize a 20C WB-06 beer at proper pitchrates after one sip (actually confirmed, haha) and at 18C-ish I'd rather brew something else..
Here's how I found out. I tasted a store bought beer which had this "spicy" flavor to it. I mailed the brewery, and asked what did you add to it? The brewer said "nothing".. Huh! Well how did you ferment it? The brewer said four days at 24C then let temperature drop.
Did the same, same spicy flavor. However. I always rehydrate my yeast, the first time I didn't because I was lazy. The second time I did, and did not get the same flavor at all. Same recipe.
So I did some testing, and found out that don't rehydrate it. A forum-friend of mine did the same recipe, but almost twice the batch size, he got even more of the spicyness on his second attempt, after I told him to not rehydrate.
Peppery (Phenolic, clove-ish) at lower and fruity at higher sounds like a saison or hefeweizen yeast.