The AMD Phenom II X2 565 features "energy efficiency innovations include Cool’n’Quiet and AMD CoolCore, which reduce power consumption by balancing the processor activity, letting you enjoy environmentally friendly, energy-efficient performance."
The Biostar A770E motherboard supports AMD Cool'n'Quiet Technology.
The Antec Earthwatt's "standby and no-load performance were both reasonably efficient, with standby coming in well under one watt, and no-load at a little under ten." [Silent PC Review]
I think most of the time the computer would be cruising along close to no-load with both the processor and power supply using very little power. Based on the
Calculate your electric cost online calculator, using 10 watts 24/7 at 15 cents per kWh the server would cost $13.32 a year to run.