heat-resistant microchips

Wat

I doubt a microchip that doesn't need cooling, while still calculating reasonably fast, is possible.

Computers use electricity to do math. The more electricity you have, the more math you can do. In order to do the math, the electricity is handled in a way that outputs heat. Unfortunately, the most reliable, cost effective and plentiful materials that allow electricity to do a lot of math also get heavily impacted by heat.