The Apex Teton is the best amp I have heard with the HD800S. With certain tubes, like an RCA 6SN7 input tube, it can be made to sound warm and engaging, though not syrupy.
DNA Audio amps are also known to pair well with the HD800s, but the build times for DNA amps are quite long right now.
I would not assume a SET amp by design will make the HD800 sound “warm”. Any amp designed around a 45 tube, which is a single-ended triode, will not sound warm, for example. It’s a very linear-sounding tube. My EC 4-45 is a SET amp that sounds great with certain headphones, but is a bit bass-shy and adds zero tube warmth, so it’s not the best match with the HD800.