I'm fond of how these conflicting yet overlapping answers point to literal language's flaws as abstractions — like a map, they point to the destination that is sound. They try to describe that sensory experience, yet utterly fail over and over... but we persist with using terms like "warm", for they are the "best" we have.
Not to dodge the question, but we are to talk about specific frequency ranges that one could alter to be "warmer", then mmm... a gentle slope @ 300 Hz would often be considered warm. Too much, then it becomes "muddy" or "cardboardy".
Or, simply using a low-pass filter to roll off the high-end makes it sound warmer. For when people equate digital to "cold" and "sterile", it is often pointed at piercing frequencies that didn't exist in prehistoric/earlier human eras.
And there is much to be said about the subtle nuances of warmth once attains by injecting your music with actual air and electricity, those chaotic forces all around us that do not live "in the box", no, they are beasts that can be bottled, if only as an echo, if only for a little while.
One of the most effective tools for experimenting with various "warmth" processes would have to be Audio Ease Speakerphone. It can do the crackle defects (but an asset if warmth if the answer) and pitch instability of vinyl. It can make any sound seem like it came from an old answering machine (a curious warmth in its own right) or a vintage microphone by way of teleportation, um, impulse responses. There are at least 500 flavors of warm in that plugin, all waiting to be tasted like flavors of ice cream, and I wax not poetic, for ultimately...
perhaps warm is like Eskimo words for snow.