You don't mention CPU performance. You can easily purchase something with an Atom that won't exceed 40W under load, but the performance will be terrible.
You can limit the power consumption of a server by limiting the CPU speed in the OS (e.g. choose the
powersave governor in Linux to force the CPU to stay at lower frequencies). The Dell R210 II idles around 20W, and if you limit the CPU speed to <2GHz you can keep the power consumption of the R210 II with an E3-1220v2 under 50W easily.
I have yet to find an E5-2600 motherboard that will idle under 40W, which is too bad because E5 Xeons and Reg ECC are really cheap.
Anyway, what's your goal of limiting the
maximum power consumption? I would focus more on idle power consumption personally.
Something like the Supermicro X10SLE-F idles at 15W, and the Fujitsu TX140 S2 idles at 18W. These motherboards are available very inexpensively on eBay (30€ for the TX140 S2) and include a BMC for remote management. You can also find cheap Supermicro chassis like the SC512.
On some Intel servers (
cough Intel S1200BTL cough) you can even edit the fan curves to keep the server quiet under load. Temperatures will rise if you haven't limited the CPU speed, but eventually it will just thermal throttle. (If you are interested in the S1200BTL with a low power CPU, I can replace the E3-1220v2 with a Core i3-3220T. It already has a modded fan curve to stay quiet.)
The HP T520/T620 are within your budget and power range. Just purchase a 1U rack shelf from Thomann and some zip ties and you're done.