Computation doesn't destroy the energy. If your system is fed by a Sun-like star you still get a Sun-like excess in radiation. At 6 K or 1/1000 of the Sun's surface temperature you need 1000^4 times the surface area, or a radius of 0.07 light years. The system would show up as an absurdly bright (~20 times the background where we look for 0.001% deviations) and relatively big spot in CMB surveys. You can change the temperature but the result won't change, you can't hide a radiation excess that large close to us. Probably not even 0.001% of it.

I've always wondered about this tho... I have enough knowledge of physics to get really confused, but not enough to understand how exactly it gets there.

There's still always heat, right? Using the energy for computation doesn't mean you're not still retaining the entire energy output of the sun inside a shell. You use the heat... But at the end you still have the heat.

Is it just that theoretically the outer shells are so big that it is simply diffusing the heat of the star across a vastly (vastly) larger area?

>The outermost layers should be at the background temperature and effectively invisible via infrared, unless they occlude something behind them.

This outermost shell would be the least powerful but also the most materially expensive to construct, due to size.

It is incredibly unlikely that a culture would want to absorb 100% of a suns energy using this method, rather than losing a few shells and not having to spend the exponentially increasing cost of new shells. Only way this works is if a species has figured out how to not have to worry about the laws of physics, in which case, why are they bothering with locating it around a specific star in the first place?