Ahh, I see what you are saying. When you refer to HF6, I assume you mean the EF-6 (which is Hifiman's current top-of-the-line amp, barring the EF-1000)? I don't think the EF-6 is particularly "cold", but I don't think that it is a particularly "warm" amp either. Definitely not syrupy warmth.
As for the source I listened to the HE-1000 and EF-1000 to, that was the new Hifiman HM901s. Definitely an impressive little player - it sounded great with the HE-400i and HE-560 directly out of its headphone jack (couldn't listen to the HE-1000 with it because the HE-1000 was terminated in XLR). I would say that the HM901s had a a very slight warmth tint to it, but not very much. So in that context, I guess I can say that the EF-1000 won't add much warmth to the music, as I felt that the HE-400i being directly driven by the HM901s in my recollection sounded slightly warmer than the HM901s + EF-1000 + HE-400i combo. (The 400i was the only headphone I used to compare those two different chains.)