Integral mass of inner planets is 1025kg. Upper bound on density of planets is 5000 kg/m3. If we set thickness of sphere to 1m, we are getting surface of 2∗1021m2, while surface area of the Sun is 6.09∗1018m2. Radius of such sphere is approximately ~ 0.1 AU, which is ~20x radius of the Sun. You can worry about too much heat, but if you can harvest atmospheres of planets, you can put all these gasses into cooling system, increasing overall efficiency.
Integral mass of inner planets is 1025kg. Upper bound on density of planets is 5000 kg/m3. If we set thickness of sphere to 1m, we are getting surface of 2∗1021m2, while surface area of the Sun is 6.09∗1018m2. Radius of such sphere is approximately ~ 0.1 AU, which is ~20x radius of the Sun. You can worry about too much heat, but if you can harvest atmospheres of planets, you can put all these gasses into cooling system, increasing overall efficiency.