Just install a low power CPU. You can get one on eBay delivered for a little more than USPS 1st class shipping. Most of my devices, including my NAS, consume 25-35w, so up to 15w additional consumption, as checked with Kill-A-Watt.
Ever do a tiny load of laundry to get one shirt clean? You've just used something like a year of computer running.
Do you run your air conditioning while your refrigerator exhausts into your kitchen? I call that a kitchen heater. You're heating a cooled space.
I find for whatever reason, tech people all worry about the energy consumed by tiny devices.
There are other power usage concerns beyond cost. For example, if a small room can't have air conditioning you might want only very low power devices to keep from heating it up.
~35 watts isn't actually all that much heat load, and that's what you get from the likes of a business-class Core i5 at the loads routing packets would put on it (i.e. basically idle). Something like Atom or AMD Bobcat is <15 watts.
Another thing to keep in mind if you're worried about power/heat is that 3.5" spinning rust can pull >5 watts per spindle. I've seen 15K drives pull close to 20. But an SSD is close to nothing and so are most 2.5" laptop spindles.
I'll concede that a small closet can get pretty warm from even lower power devices. However, as long as the CPU isn't overheating and the space is clean and dry, it doesn't matter.
Ever do a tiny load of laundry to get one shirt clean? You've just used something like a year of computer running.
Do you run your air conditioning while your refrigerator exhausts into your kitchen? I call that a kitchen heater. You're heating a cooled space.
I find for whatever reason, tech people all worry about the energy consumed by tiny devices.