A warm DAC?

What you’re looking for is a Meridian DAC The most tubelike SS DAC out there. To get the best out of it, cabling is critical however, I have an 808 but the ultra DAC is very similar & likely better still. There’s literally no more musical DAC - but not coloured. Very detailed as well. Arguably the MSB DACs & a few others are excellent too but as for musicality (w/o sacrificing much if any in the way of detail), it cannot be beaten. Please don’t take my word for it. Go listen for yourself. Read the Stereophile review for starters >
https://www.stereophile.com/content/meridian-audio-ultra-dac-da-processor
The DCS Rossini he mentions may be accurate but not nearly as musical having a whitish sound (I heard it with the optional clock). When you listen to it, make sure it’s with other than Meridian cables & of the highest quality. The better Kimber & Nordost Tyr or above work well.

I don't know what warm sound is unless you want 2nd order distortion versus odd order distortion which sounds brighter.  As to a neutral but very full sounding DAC, I can recommend the COS Engineering D1.  Their H-1 is more open but much less full sounding.  I own the D-2 which is in-between, quite full sounding but not quite as open.  The price differences are significant with the D1 at $10K and the D2 at $5k, H-1 at $2.5K(?).  I'm coming from an EAR Acute, my former "warm" sounding tube CD player.  The greatly improved micro details, more open soundstage made the D-2 my choice over my 15 year old CD player.  All three models are not too far forward or too far back from the speaker sounding, just right in the middle, permitting the recording soundstage to reproduce more accurately.

@nicktheknife
The best way to find out is try different cables and see if you can tell a difference.  Try to control for normal human biases as best you can.

@surfmark. Couldn’t agree more! 

For your purposes the PS Audio DAC III is a warm DAC and probably quite affordable used if you can find one.