How 'bout I apply my critical thinking skills to your post, instead?
I'm pretty sure a decent engineer with a budget as big as NASA's could build something that survives that kind of oscillation of temperatures.
Although, also, I don't think you have the physics right if you think any part of the ISS actually suffers that; in a vacuum, the energy in a hot object can't go anywhere very fast except via the space station's own cooling system - the only other outlet is radiation, but objects at 400K don't glow that bright.
The numbers you've got there are, I think, the average of the sun-facing side and the average of the shadow side. The actual temperature change the sun-facing side undergoes between sunrises is much smaller.
RE: Solar panels don't work in extreme heat. This has a point.