Not sure how you're drawing this conclusion. Let me try again --
I think what you're talking about is all one and the same thing -- they aren't two separate issues to my mind. From my perspective, the patterns in the OP's soap are an example of "glycerin rivers" and "rivers" are created when soap made with different fatty acids crystallize in various opaque and translucent patterns. I hope this helps.
(I don't like to call this "glycerin rivers" because the patterns are not made of glycerin. It's all just normal soap. I'll compromise on calling them "rivers.")
If you're fats aren't fully melted and clear at the time you add the lye, working a bit warmer might be helpful. Otherwise, no, I don't think warmer temps are going to prevent this.
Rivers are created when soap goes into gel and then it cools slowly. All soap forms crystals, but sometimes they're small enough you can't see them; sometimes they're more visible. Rivers form when the liquidy soap cools slowly enough to form larger crystals that are visible to the naked eye. Pigments (titanium dioxide in particular) can make rivers more visible, but you can get rivers in pretty much any soap, with or without pigments.
Variations in the fat and water content of the soap batter can create rivers and other types of visible variations in the appearance of the soap. I think that's the basis for PenelopeJane's comment, Post #10 above. If you look near the bottom of the soap bar in the photo, you'll see a slight orange tinge to the white portion which might be a bit of batter that's slightly different than the rest. Before pouring soap batter into a mold, it's good practice to scrape the sides of your soap pot with a spatula and mix the scrapings into the main body of the batter.
More: https://classicbells.com/soap/streakMottle.html
