Should my Dyson Sphere be bigger? (Climate/habitable zone)

My world is a 1AU radius, 12000km thick Dyson Sphere with 6 equally spaced holes, 4 filled with water. The two main problems I have are gravity and heat. This question concerns heat and how to stop everything on the inside from being incinerated.

The majority of the inhabitants live on the inside of the sphere, so it is perpetually day. This means they are constantly heating up. I designed a heatsink to deal with it but I don't think it's enough.

Would making the sphere bigger (like, TNO bigger, there are no planets in this case) mean less heat is generated per square meter? There would be more surface area for heat to dissipate.

Our solar systems habitable zone is where it is because of the surface area of the planet so would making a DS move it out further?

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Should my Dyson Sphere be bigger? (Climate/habitable zone)

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