I'm an EE and have made an honest exploration into this topic many times, and yet still have no explanation of "warmth" beyond the addition of distortion resulting in even-ordered harmonics. Which is precisely a decrease in the SNR from input-to-output.

That might sound good! But it's a less-than-perfect reproduction of the source signal.

If there's a better explanation than what I've come across every time I've search for this, I'm all ears and honestly open to being corrected.