Can you suggest a warm high-end CD player?

Not going to argue the merits of the APL denon 3910 versus the Esoteric X-03. However, just from a features standpoint, the Denon 3910 plays more formats than the Esoteric X-03..DVD, DVD-A, etc.

Is the Esoteric considered a warm sounding player?

FWIW, I don't consider the APL Denon 3910 a warm sounding player...natural sounding, yes. I have heard warmer digital players, namely the Marantz SA-14 and the Modwright Sony 999ES.

try a california audio labs tempest or aria.

your right, the Ayre CD 5 xe is not exactly warm, but in part it depends on the equipment it is paired with, as well the speakers. As well, eraticating all emi and rf will further the chances of this piece to be warm. I think it is warm but all the other pieces of the puzzle need to be in place. Neutral is a fair consideration of this piece overall. well done

I would highly recommend the Cary 303 or 306. The Cary house sound is a little on the dark side with a very nice, warm midrange.

another cd player to consider is one of the older metronome.
how about the top of the line lector ?