I love the Music Hall player, which I consider pretty warm to start with. Certainly the excellent suggestions here would be warmer still. I have listened to the Jolida and didn't like it as much as the Music Hall -- too mushy for me -- but it may be just what you are looking for.
Here's the point of my post, though. You might want to think about replacing your receiver rather than your CD player. I was astonished at the difference replacing a receiver with a good pre-amp and amp made for me. I have listened to the NAD integrateds (not receivers though)pretty carefully, and they just aren't up to the caliber of your existing CD player IMHO.
The result might or might not be "warmer," (depending on the equipment you choose), but I bet you'd like the result. It would be great if you could demo some alternatives in your environment somehow.
My gut feeling is that spending $1000 (used price) as you could with some of the CD player suggestions above will be wasted (well, not give you the full benefit of your investment...) with your current amp setup.
Another thing to consider is your room. Perhaps there's some harshness there you are (over-)compensating for? Are carpets and heavy drapes called for?
Just trying to think outside the box a bit....
- Eric