Warm, rich, smooth, 3d tube integrated amp, budget $6000

@vassilis_t cool another ns5k owner... thanks will look into those 

@sandthemall ya evo 400 looks like a great amp.. definitely on my list.. I haven't seen too many comparisons to other amps tho 

+1 on the CANOR AI 1.10. Have had the opportunity to listen to it at length with Aerial Acoustics, Revel & Sonus Faber and it's been equally magnificent with each. Those are all pretty different sounding speaker brands with their own signature sonic footprint but the Canor was liquid although highly intricate with each. There are many excellent brands in this $6K+/- space and members have touched on many: Aesthetix, Octave, etc. I'm a big fan of Audiomat, Unison and Manley too. They also have wonderful integrateds at that price point. New/used so many great options. GL!

FYI tubes get super hot.  That's what they do.  The more tubes, the more heat.  If you want a "cool" tube amp, try solid state (but not Class A)!

I am a broken record on this, but, the integrated tube amp that I am a BIG fan of is the Synthesis Audio A-40 (40-watt, pushpull, KT-66 tube).  It comes with a killer good DAC included

I agree with the above statement. I have a Synthesis Audio A-40 that powers a pair of Audio Note speakers and the sound is just sublime. Feel free to PM me if you would like any additional info. 
john

Prima Luna Evo 400 fits all your requirements. And it drive pretty much any speakers. If you change the two front 12AU7 by NOS tubes you get even more sound space. Highly recommended.