I've run my Q701 from something as simple as the Fiio E11 and even my E10 and upwards of a Schiit Asgard & Lyr and frankly, it's not that big of a difference, if any.
Ultimately I find it's still just not that warm, not even as warm as my Hifimans (300/400/500). It drives fine from a lower powered source. I don't think you need massive amping to really get the worth of the Q701. I also don't think a warm tube amp helps much. But that's just my experience with it from several of my sources. I like the headphone, the Q701 is fantastic. My only beef with it is that it's just not warm enough for me, even though it's a little warmer than the K701 which was just too thin.
I'm pairing a Schiit Lyr (stock tubes) with Q701s at the moment. Source is an HRT music streamer 2. The interconnects you use make a big difference IMO. I'm using Kimber KS1030 interconnects and the sound is so sweet, warm and musical.