A pity it's got to be that low -- Atom Z2460 has a TDP of 4w... it's an SoC Atom from what I understand -- meaning no chipset, just add RAM, VReg, and a few interface bits.
But there's no way to keep the required external components less than a watt, I'm sure.
Worth noting, even VIA can't keep up with that. Closest is an Eden ULV 1.0GHz Esther core... it gets 3.5w TDP but that's before the chipset and everything else...
Oh well :(
Just a thought -- I forget -- are EOMA68 cards permitted to protrude from the slot any, the way PCMCIA/Cardbus cards almost always did? If so, it *may* be possible to wire up a small ventilation system -- fan with a bit of ducting is what I'm picturing, there's no room for a real heatsink in there, after all. But every little bit helps... ;)