A sphere rotating in a vacuum should still experience black body radiation and gravitational drag. Damn kids and their pesky attempts to violate the 2nd law.
Cooling down would not slow down the sphere, if the radiation is uniform.
Gravitational drag, maybe, but only if there is something to drag nearby, and we postulate a vacuum.
A sphere is symmetric and thus does not emit gravitational waves.
I wonder if an effect akin to black hole evaporation could play a role: if one of the two virtual particles gets accelerated towards the sphere, it may bring some momentum to it. But, assuming that the space is isotropic, statistically such momentums should cancel out.
A vacuum doesn’t exist in reality. In addition to virtual particles, gravity travels forever afaik. Which means your rotating sphere will interact with matter no matter how far away it is. Unless you’re hypothesizing a universe that doesn’t exist. In which case, we can also hypothesize one where the 2nd law isn’t an issue.
Also, I’m not so sure that black body radiation wouldn’t have an impact on rotation. At some point, the object will have radiated all its heat and have no energy left. If the particles have no energy, how is the sphere rotating which implies kinetic energy? That implies that even when radiating uniformly, black body radiation must take away angular velocity, no?
A source of free energy, a "perpetual engine", is indeed impossible.