[galaxyLogic]

> It would, like your eyeball, get the light of the stars from all directions, and would soon equilibrate to the same temperature

I see, that may be the crux of the paradox.

But if we assume that stars were born at some time then dark planets could be too. And if stars became to existence at some time it is not too crazy to think that new stars might be continually become into existence and planet too so new planets would get created continually to block the light.

[improbable22]

If there's a time at which the stars are born, then there's no paradox. Non-star things can stay cold for the same reason comets stay cold in our universe: they can radiate heat in almost all directions (into the black sky) and receive heat from only a few (like the sun on a brief swingpast, still only < 1% of the sky).

But if the stars have been there forever, the comet is effectively in an oven of uniform temperature. The equilibrium state at which it radiates heat as fast as it gets it has the comet's surface the same temperature as the rest of the oven. So it glows.