How about putting the ice maker portion into a container (within the refrigerator), fill the container with antifreeze or alcohol and put a coil of copper tubing into the liquid. Through the copper (or stainless steel) tubing would pass the coolant for your water block.
You could also put a small pond pump in the container to circulate the cold medium to make it more efficient. The temperature setting of the refrigerator would need to be set to a point that did not freeze your water block coolant when your computer was switched off, otherwise you'd have no circulation after a while. It may be preferable to use the same coolant throughout. The biggest headache would be insulating the tubing from condensation.