I'm just going to chime in and echo what krunkie mckrunkface has been considering. I believe that cold to warm is going to provide a more thorough extraction of the good, without going to far and extracting all the oopsie. And the more you go from cold to warm to cold to warm the more you will extract. Obviously it's kind of pointless unless you are seriously trying to conserve. Warm to cold to warm might be the best but I've yet to try that.
I'm no expert and fairly new to kava in general. First experience was probably in like 2017, so take what I say with a grain of salt.
Using an aluball:
I've found that if you'd start with cold + have a fatty substrate, whole milk works best, but some coconut oil does the trick. Agitate and let sit in the freezer or fridge for a bit until you start to see the oil solidify. Agitate and wait (or not. doesn't take long). (Before you let the solid oil bits melt, if you take a spoon and scrape them off the sides you'll notice they pack a punch.) Then take it out and continue to agitate and you will notice the solid oil bits start to melt slowly over time. They will begin to combine into an oil. This seems to do something, not sure what, but you will notice a thick film of oil forming at the top.
So my conclusion is that it's definitely not either/or, it's for sure both and ultimately preference, convenience, etc. I do notice that there are various "qualities" to the potion, some I'm sure have more to do with body composition and gut microbiome diversity than what you're getting out of the agitation. However, there does seem to be more euphoric and uplifting forms that the KLs take and also more sedating and trippy they take as well. It's not mutually exclusive, but for me the sedating feelings are more "trippy" and the uplifting feelings are more "euphoric". I might just be saying nonsense so I'll shut up for now and see what kind of response I get.
Oh shit and I just realized this thread is from 2017 so probably none, lol