Dyson sphere
The innermost Dyson sphere of the Matrioshka brain would draw energy directly from the star it surrounds and give off large amounts of waste heat while computing at a high temperature. The next surrounding Dyson sphere would absorb this waste heat and use it for its computational purposes, all while giving off waste heat of its own. This heat would be absorbed by the next sphere, and so on, with each sphere radiating at a lower temperature than the one before it. For this reason, Matrioshka brains with more nested Dyson spheres would tend to be more efficient, as they would waste less heat energy. The inner shells could run at nearly the same temperature as the star itself, while the outer ones would be close to the temperature of interstellar space. The engineering requirements and resources needed for this would be enormous.