Is "warm" a compliment or a criticism?

At the least, "warm" means that the sound is not shrill or harsh. Most anyone would consider that great news. But beyond that, the meaning seems to depend on writer / speaker and the situation. A system that portrays the beauty of midrange, such as female singer or sax, can be described as warm. But "overly warm" suggests that details are being sacrificed in exchange for presentation of a sound that is pleasant, but lacking in realism.

For many years, it seemed that most transistor gear had a harshness or graininess to it, and so "warm" was a welcome relief from this problem. Todays best systems seem to sound realistic without being either grainy or overly rich or colored ("warm"), and hence this term can had positive or negative connotations.

While Jeffreybehr makes a valid point regarding a possible hump in the FR between 100-300Hz (that could be even "lumpy" for some people) or alternatively a notch in the 2-6kHz region, IME the term "warm" is usually used in a positive vein:
the sound is full "enough" -- i.e. there's sufficient energy but not more than necessary -- in that region.

Mind you, one person's "warm" could be the next person's "lumpy" ESPECIALLY relative to the spl at which this comment is being made: at low spl our ears are less sensitive at 100Hz than they are at 3kHz!

One man's ceiling is another man's floor-Paul Simon

It's usually neither. It is more like a benchmark as with dead neutral as the center. Krell preamps have had the reputation as being stark, cool, tremendous base slam. Where the top end Classe preamp, has been descriped as warm, rounded,laid back similar to Rowland equipment. None of the aforementioned descriptions are positive or negative, just a positioning on the neutral continum. It does turn into a negative when a Reviewer states that the sound was too cool or too warm. As in most things who is to say what is dead neutral. Everyone has their own perspective of what a system is supposed to sound like. Whether your system is yin or yang, if your tapping your feet to the music, who cares.

Gunbei, Are you having a Wierd Science kinda day? All your posts are Female Part's related? Feet, Curves, Etc... Could get somewhat Warm if your sitting in front of your computer with a Wonder-Bra on your head, designing the Perfect Woman.