Following this video, @Linda Linsefors and I tried to make a phase change material with a freezing point around 18°C.
Report:
For our first batch (which is all we've made so far), we started with 2 l water / 400 ml sodium sulphate / 100 ml table salt. There was a lot of salt left over after several minutes of stirring boiling/near-boiling water, so we added another 500 ml water. There was still a lot of salt but we stopped there.
We added 30 ml xanthan gum. (By the recipe it should have been more like 40 because of the extra water. The goop we ended up with is pretty good goop consistency, but I do think I'd prefer slightly thicker.) The first teaspoon clumped up a lot in the water, so later ones we ran through a sieve which helped a lot.
We boiled and stirred that for about 30 minutes and left it to cool.
Note that sodium sulphate comes in "anhydrous" and "decahydrate" forms. The latter already has 10 water molecules attached, so less of it dissolves and you get less actual salt. We used anhydrous. I kind of assume the guy in the video used that too (it would be weird if he got better dissolving than us with decahydrate) but idk if it's clarified anywhere. It's presumably possible to use decahydrate if you adjust quantities appropriately.
We got something that kinda worked, but I was suspicious that it wasn't behaving like it should, so I got a temperature logging probe (note: needs initial setup with software that's available for windows or mac, not linux; I used wireshark to capture the USB traffic so maybe I can make linux software but it's not a priority). Here's the graph when I put some of it (at a guess about 50 ml) in the freezer and then thawed it:

So yeah. The thing around 3-5° going down could be either freezing or "freezer is temporarily off (as I interpret the rises later on) but ambient temperature is low enough to keep cooling". Claude thinks there wasn't nearly enough sodium sulphate, and it's basically just salty water, which freezes at that temperature; and which apparently has a smooth melting curve. Conversation (I mistakenly said 60 ml xanthan gum there). I'm not very convinced by its recommendations.
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We separately wanted to see what happens when you just mix sodium sulphate and water, because something that freezes at 32° sounded cool. We started with 200 ml water, tried to keep it around 40°, and added sodium sulphate until it stopped dissolving. That ended up being about 80 ml. It should support about 100 g. Google gives density of the powder as 1.4-1.6 g/ml (a crystal is about 2.7 g/ml) so we'd be at about 120 g, there are enough errors in the process that this doesn't seem off to me.
What we ended up with was something that freezes in the fridge, but not at room temperature (which was about 28° when we tried). I'm currently thawing it so I can put the probe in, and then I'll freeze-and-thaw it again and see what happens.
I think it took a few freeze-thaw cycles before it seemed like it would fully freeze? First time it looked more like "clear ice with some water not yet frozen", now it looks like white ice.

e: okay, it hasn't thawed at all after several hours. I'm pretty sure it just actually freezes above room temperature, and what I saw before was probably just some combination of supercooling and "not fully saturated" and idk what else.
Hm, so I hadn't actually touched it, and when I did it was kinda squishy, which made me think "maybe it did melt, and the gum just made it keep its shape"? Anyway, I put it back in and out of the fridge with the thermometer, and

So... it looks like it did freeze at 18? But then still doesn't have an obvious point where it's melting, which, ???