I don't understand your argument. Sounds like you're saying, "In theory it should work, but what if there are space pixies that keep rebooting the TPUs? What do we do then?"

The 15-minute figure is what they currently designed for because they have mass constraints. If they wanted a different figure (like forever) they could do it with a larger radiator.

As you said, the physics is solved! We know exactly how much heat a surface radiates in space--there is literally an equation for it. We know how to cool stuff in space. Will the price be low enough to make a profit? That's the real question. But stop worrying about cooling in space.