Part 2 - adding the fan.
I actually expected that this might happen. The Dynatron heatsink is really a 1U server heatsink and it needs airflow to carry the heat off the CPU. There isn't room for a truly passive heatsink in the M350, but since I'm not installing any hard disks there is a bit of space to work with.
The big Shuriken I had left over from a prior build wont fit...but that slow quiet 120mm fan on the Shuriken will. So I mounted to the cover of the M350 with rubber fan mounts. At first I thought I'd have to drill out holes for the fan mounts, but turns out the rubber mounts pull through the grill on the M350 just fine.
Fan and mounts

Mounted to lid

Everything all buttoned up

The M350 is ugly as sin, but its small and compact and with its VESA mounting holds will mount under the desk. Almost invisible.
Running Prime95 for 24 hours the peak core temp recorded as 85C with an average of 81C. Still pretty warm, but well within Intel's operating specs. The MB built in speed control runs the fan at about 800 RPM and is near silent. When running Prime95 it sped up to just over 1000 RPM but was still inaudible.
Also interesting - when running Prime95, both cores showed that they were operating at 3.2Ghz, +0.3Ghz turbo boost to both cores at 85C. Nice!
Got ESXi loaded. Loaded the after-market drivers for the 2nd NIC so ESXi sees both.
Also took some power readings at the wall with a Kill-a-watt:
Power brick vampire power: 2W (not even plugged into the computer)
Windows full idle, video off: 12W
Windows idle but video on: 17W
Windows with light work (firefox browsing): 21-25W
Windows, full load, Prime95: 57W
windows, full load, Prime95 but video off: 52W
ESXi, idle, no VMs running (no video): 15W
ESXi, near idel, one Windows VM running: 20W
Power levels are a bit higher than I expected, especially at idle. Don't quite understand why ESXi idle draws more than Windows, but I probably won't care about a couple of watts.
I'm still not happy. I really need it to be fanless. The area under the desk is dusty and with animals in the house there is lots of loose pet hair. Anything with a fan quickly clogs with dust and hair. I've ordered an Akasa Euler to put it in fanless. Will update pictures when I move it around.