Are tubes really “warm”?

It all depends on the type of tube and it's implementation as you surely know. Warm to me means mid to upper bass emphasis or "dark" An EL34 can sound "warm" Tube sound to me means natural tone and body; two things I really like.

This old adage goes back to when most amps were tube-based and used in systems with limited frequency response. Components like carbon resistors, saggy resistor voltage droppers, and tube rectifiers contributed to this ’tone’ of a rolled off upper treble and woolly bass.
In reality, a good modern tube amp has a certain naturalness which can be attributed to lack of solid state transistor haze caused by switching noise and its associated odd-order harmonic distortion. With modern components, tube amps can sound as cool and neutral as you prefer. Conversely, many solid state amplifiers can  sound warm so it’s not a predictable way to classify the type of sound you’re going to get from a specific type of amplifier. To add complexity to the issue, electronic passive component and tube type, configuration and brand selection can also affect how warm or cool an amplifier sounds. 

Of course if you’re going to play CDs with them it doesn’t really matter since CDs are lacking in warmth and air anyway. You can’t turn a pig’s ear into a silk purse. 🐷 

Not with Audio Research. They make tube gear that sounds like solid state. Never understood this brand. 🙄 Why use tubes in the first place if you aim for a solid state sound ??...

Good post @noromance 

The tube sound for me has always been about the presentation, not the linearity of its FR.  There is a holographic nature and weight to images that can be tough to get right with solid state. For me, if a tube amp sounds 'solid state', it means there is no real soundstage depth or weight to images - a flat sound if you will.  Some tube amps do sound like that, and the opposite is true for solid state amps sounding like tube amps, but it is much rarer to find the latter.