[Karellen]

One solution to this is the Matrioshka brain, which consists of many nested "shells" around the star. Each one absorbs the radiation from the hotter shell inside it (or from the star, if the inner shell), and radiates waste heat to the cooler shell outside it. The temperature differential between the inside and outside of each shell is what allows work to be done. The outer surface of the outermost shell, maybe 5 billion km (~35AU, or a bit further out than Neptune) from the star, will be close to the ambient temperature of the interstellar medium, and will radiate heat at only a few Kelvin into it.

https://en.wikipedia.org/wiki/Matrioshka_brain

[micw]

So instead of seing a hot "small" spot (the star), we'd see a warm (a bit above absolute zero) but very large sphere?

[javcasas]

Well, seeing it may be an exaggeration. It would be barely less black than the space around it. Though it may shadow other stars and distant objects.

[quadragenarian]

Isn't the point (and I could be wrong) with a Dyson sphere that it should have a spectrum that approaches that of a perfect blackbody radiator? Or would any radiation that sneaks past the swarm drown out the blackbody spectrum?

[javcasas]

> Isn't the point (and I could be wrong) with a Dyson sphere that it should have a spectrum that approaches that of a perfect blackbody radiator?

Pretty much. The lower the temperature of that blackbody radiator, the higher energy you can extract via temperature difference. Until you reach the background radiation of the universe, which could be considered the lowest possible temperature of a thing that still extracts energy.

> Or would any radiation that sneaks past the swarm drown out the blackbody spectrum?

If that's the case, you can improve your sphere and capture that extra energy.