The Modi is not a cold dac at all, in fact I might say it's a pretty warm dac. It became certain to me after I got the DM100 that the Modi leans more towards the dark side. The Magni on the other hand, I can't recommend for the Q701. Tried it, regretted it.
Have you tried the ODAC? The ODAC is actually colder than the Modi, but I can't put them into the warm/cold category. Both seems neutral enough to me.
I don't find the Modi warm since it sounds great with the HD-650 and darker headphone. However it DOES seem to be slightly warmer sounding than my Headroom Micro DAC (which uses the CS4398).
Modi is definitely not an analytical sounding DAC, which is good for me. Same with the ODAC.
BTW I just now realized what the DM100 was and that you had a T1. The only time I found some slightly warmth hidden away in the Modi was when I used it with the T90! Not sure how that compares to the T1.
I just know that the Modi is not dark enough to reduce the treble on the Q701 or make it less bright. I haven't tried it with the DT-880 though or a Grado SR-325is.
I do think the Modi might be a good match for the HD-800. It might take the edge off that. Not like many people use a $100 DAC with a $1500 headphone though!
For reference I found my E17, E10 loaner and even the HRT MSII to be darker than the Modi. MSII seems to be warmer than all of them and has a small soundstage IMO.
I didn't realize what I was missing on the Q701 until I tried the ODAC and then later side-graded to the Modi (which I found slightly better).
I also didn't like the Magni with the Q701. I had a very early version though. Vali is a much better match.
When I get rich I want to try the Lyr or Valhalla with the Q701. The trick is finding out which of those will also sound good with my HD-650.