What I mean by Warm Sounding Speaker.

So well said i will not add anything...

Perhaps  i will speak instead of a speakers/room "warm" or "cold" potential delivering according to the recording trade-off  ... But the OP is speakers designer and speakers own a design of their own then i get his point ...

I can name a number of mid to high end speakers with small rises and dips in small bands which I believe contributes greatly to their signature, and probably their success as well.  

I want to make it clear that warm is not flat, nor is cool flat either.  The frequency troubles I am talking about happen within an octave or two, they are areas where the speaker will sound like it has more detail than others exactly because of these little peaks and valleys of reproduction.  

To be a warm speaker is to be a very smooth performer, with no particular area more prominent.  For instaace, if I notice excess chest sounds, or resonances in the lower female voice, particularly plastic sounding reeds, which may sound more natural if my ear was on stage.  Also, not warm are systems that have one note bass.  A warm sounding speaker should have unique tones for each performance, not color each performance with it.  I know this sounds counter intuitive, but a warm speaker doesn't make Gwar sound warm, but rather it has the possibility of sounding warm when the source is warm.  

There.  Now that I have perturbed the waters of A'gon I can get a good night's sleep.  

 

In agreement with you on your definition of warm

I would add:

I think you can make warm music/production sound warm but you can’t make  neutral or cold music sound warm. Effortless mids and relative lack of highs and a compound sound vs a lot of separation is what sounds warm to me. 

One thing supporting this theory: vinyl sounds warmer, always. (Honesty, I am just saying stuff I feel, no science in my brain)

I agree with the OP on this. That said. a "perfect" speaker would output simply what was fed to it, nothing more or less. I've said this before and drawn criticism for it. Audiophiles chase whatever distortion suits their ears.  

“Warm” is created by an elevated midbass and a dip in the presence range, combined with a gently sloped upper end rolloff. The bass boost acts as a sort of built in loudness compensation, as most home listeners play music below the equal loudness threshold. I prefer a flatter response but don’t object to the gentle rolloff above the midrange, as many classical recordings are too closely miked for my taste, and the tilt helps mitigate the effect. 

I like “natural” sounding sounding speakers so good recordings just sound “right” to me, which admittedly may sound warm or cool to someone else cause it’s a moving target based on personal tastes/hearing.  “Warm” or “cool” to me implies a coloration of some sort one way or the other.  That’s all I got.