Warmth need not be distortion... but accurate musical presentation.
Long ago tube amplification excelled at rhythm and pace and midrange bloom. This part of the spectrum communicates the emotional content / connection with the listener. But it was not good at the detail, it was soft in the treble and slow with the bass.
On the other hand... solid state gear was very strong in treble... often etched and very quick to put out power to the lower frequencies.
Neither sound was satisfactory. But over the decades by design the sounds converged with audiophile tube equipment added detail without loosing the beautiful midrange and solid state gear was designed to provide better midrange and not be too hot in the upper frequencies.
Largely the two have now converged. But there is still a tendency for solid state to be a bit too detailed... not too detailed, but present details too highlighted versus the tube equipment and not have the rhythm and pace of real music. But things are so much better.
To me, tube gear still has the edge (by companies trying to portray music accurately) in getting the gestalt and the details right in musical reproduction. Many solid state exploit their ability to highlight detail and image, but loose some of the intimate magic of realistically reproduction of music.