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[–] The_Cat ago 

Possible, though if you want to cool such a massive structure in the vacuum of space, you'd probably want to radiate away waste heat all over so your equator doesn't melt.

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[–] nicethingyoucanthave ago 

It radiates some heat from the equator. But most of the energy collected from the star inside is moved to the poles. That's where their industry is. Thus, if you viewed the system from above its pole, it would be brighter. If you view it on edge, it's a bit dimmer.