Your argument is complete nonsense, like asserting in the 19th century that airplanes and air travel make no sense. Dismissing is easy; being an inventor takes work. If people listen to you, we will never become a Kardashev II civilization, and it'll be your fault.

There is plenty of scientific literature on the topic of cooling hot materials in space. Moreover, the research is not finished -- it will continue to progress. I surveyed the current works, and put together a video to communicate the salient points:

https://youtu.be/s7Mv_OcBXI8 ⤷ Engineering Constraints of Orbital Space-Based Compute: Heat Rejection and more

NIMBY = Not In Mars Back Yard

Where does the heat always go? It goes into the environment. In space the environment is space. It goes from high-temperature GPU made for space to a large metamaterial coated heatsink with optimal geometry to radiate into space.

That is a great question, and materials are still being researched to dissipate heat effectively in space. Meanwhile, I put together this brief video to document the current understanding:

https://youtu.be/s7Mv_OcBXI8 ⤷ Engineering Constraints of Orbital Space-Based Compute: Heat Rejection and more

Excavating that much volume would be a heck of an expense.