And that leaves you with how to dump the heat out of the water, and that is most effectively done (in a small scale) with thermo-electric coolers. You can add scale cooling very effectively by turning on additional coolers. My design is pretty simple, the reservoir tank is on top of the rack and there is a heat exchanger on the bottom and one in "front" of the CPUs. As they draw air through the heat exchangers the water warms and rises to the top where the reservoir is, and the chilling water in the reservoir naturally sinks back down to the bottom where the first heat exchanger is.
You can think of it like a rack sized version of the liquid cooler you can put on an enthusiast PC these days. Its quiet, self contained, and quite efficient, while still being able to use forced air cooled server equipment. The goal being efficient cooling in a temperate climate (California Bay Area) that is quiet and can use surplus/old equipment that was originally slated for a data center without violating any of that equipment's assumptions about the environment it can count on.
What standard are you using for "efficient"? Thermo-electric coolers are neat, but the last thing they are whatsoever is efficient from a power-usage stand point.
If you're doing chilled water cooling, the only real option to consider is a mechanical heat pump (e.g. the ones in a refrigerator), but even that is silly. Hardware doesn't mind being somewhat warm, and using ambient air for cooling is far more efficient then either.
There's a reason thermoelectric refrigerators aren't really a thing. Peltiers are horrible. Mechanical heat pumps easily achieve twice the efficiency or more.
PUE
This is the part that sounds strange to me. Water cooling has its advantages, but the heat is almost always dumped from the water by pumping it through a radiator that has fans blowing air through it. What's the advantage of thermo-electric cooling here over the traditional method?
1) It is quiet
2) It is easily electronically controllable based on the heat load in the water.
The heat sinks on the thermo-electrics are convection cooled and you could blow air over them but as you increase the thermal gradient between the heat sink and the air around them you are able to dump more heat. The only parameter you can vary with the typical heat exchange is "blow more air" you can't change the working temperature of the exchanger.
That said, the way power plants cool their water is in big evaporative cooling towers, but since I don't need a humidifier for the lab I stick with just convection cooling :-)