As a true cynic, warm, to me, means just enough 2nd harmonic distoetion, such as Conrad Johnson and Audio Research have been purported to intentionally add to their designs.OK. With respect, you need to read up on the inherent electrical characteristics of solid state and tube amps. But absent your doing as I suggest, how about instead, I throw out some casual off-the-cuff remark that Levinson, D'Augustino, and Ayre intentionally add odd order distortion to their amps? Not true, but equally valid and analogous to your remark.
Now seriously, some tube amp manufacturers strive to minimize second harmonic with ultralinear pentode-based negative feedback designs and others strive for other design goals. You named the wrong manufacturers for the former, though there were admittedly a product or two from each that may have fallen short, particularly C-J preamps of old.