"The energy ratio is 3.5/1. We should use nuclear to provide the energy put into the rock. It's cleaner, abundant, and it can't fuel your car while gasoline can."
Might be able to use the high temperature gas reactor to provide process heat, it could produce electricity as a byproduct.
I'm suspecting that they're doing this with a heat pump. Where they extract heat from the perimeter, causing ice, and pump into the center for the heat.
If they used two sides of the existing ice wall when they moved the production hole, that would save some. And they could also extract energy out of the abandoned hole by running the steam generated by the cleaning process through a turbine. You wouldn't be able to extract all the energy out that you put in, but perhaps enough of a percentage to help out.